Algebra and Trigonometry Enhanced with Graphing Utilities (7th Edition)

Chapter 2

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; The given trinomial follows the form , where ... more

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; The given trinomial follows the form , where... more

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; Apply the property of zero-product to find ... more

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; Since the expression includes more than one ... more

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; The given expression is in the form , where . ... more

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double root ; Since the degree of quadratic ... more

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discriminant ; The discriminant is the part of the... more

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Quadratic equations can have one, two, or no real ... more

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First-degree has as the highest power and is ... more

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Standard form of a quadratic equation is always ... more

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; Factor. ; Set each factor equal to zero. ;  or... more

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; Factor. ; Set each factor equal to zero. ;  or... more

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; Factor. ; Set each factor equal to zero. ;  or... more

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; Factor. ; Set each factor equal to zero. ;  or... more

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; Factor. ; Set each factor equal to zero. ;  or... more

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; Factor. ; Set each factor equal to zero. ;  or... more

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; Factor. ; Set each factor equal to zero. ;  or... more

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; Factor. ; Set each factor equal to zero. ;  or... more

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; Factor. ; Set each factor equal to zero. ;  or... more

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; Factor. ; Set each factor equal to zero. ;  or... more

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; Put the quadratic equation in standard form,  ... more

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; Put the quadratic equation in standard form,  ... more

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; Put the quadratic equation in standard form,  ... more

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; Put the quadratic equation in standard form,  ... more

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; Put the quadratic equation in standard form, , ... more

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; Put the quadratic equation in standard form,  ... more

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; Multiply both sides by  to transform the ... more

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; Multiply both sides by  to transform the ... more

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; Multiply both sides by  to transform the ... more

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; Multiply both sides by  to transform the ... more

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; Take the square root of both sides (don't ... more

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; Take the square root of both sides (don't ... more

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; Take the square root of both sides (don't ... more

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; Take the square root of both sides (don't ... more

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; Take the square root of both sides (don't ... more

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; Take the square root of both sides (don't ... more

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; The equation already has the form , so complete... more

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; The equation already has the form , so complete... more

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; The equation needs to be in the form , so add  ... more

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; The equation needs to be in the form , so add ... more

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; The equation needs to be in the form , so add  ... more

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; The equation needs to be in the form , so add ... more

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; With the equation in standard form , find , , ... more

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; With the equation in standard form , find , , ... more

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; With the equation in standard form , find , , ... more

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; With the equation in standard form , find , , ... more

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; With the equation in standard form , find , , ... more

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; With the equation in standard form , find , , ... more

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No real solutions ; With the equation in standard ... more

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No real solutions ; With the equation in standard ... more

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; Write the equation in standard form by adding... more

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; Write the equation in standard form by adding... more

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; Write the equation in standard form by ... more

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; Write the equation in standard form by ... more

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; With the equation in standard form , find , , ... more

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No real solutions ; With the equation in standard ... more

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; To remove all fractions from the equation, ... more

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; To remove all fractions from the equation, ... more

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; To remove all fractions from the equation, ... more

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; To remove all fractions from the equation, ... more

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; Distribute on the left and simplify. ; Subtract... more

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; Distribute on the left and simplify. ; Subtract... more

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; To remove all fractions from the equation, ... more

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; To remove all fractions from the equation, ... more

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; To remove all fractions from the equation, ... more

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; To remove all fractions from the equation, ... more

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When the result of the discriminant is greater ... more

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; Add  to both sides to get the equation in the ... more

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; Add to both sides to get the equation in the ... more

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; With the equation in standard form , factor. ; ... more

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; With the equation in standard form , factor. ; ... more

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; With the equation in standard form , factor. ; ... more

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; With the equation in standard form , factor. ; ... more

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; Subtract from both sides and arrange the terms... more

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; Subtract 2 from both sides and arrange the ... more

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; Subtract from both sides to get the equation ... more

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; Subtract and subtract from both sides to get ... more

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; Subtract from both sides to get the equation ... more

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; Subtract from both sides to get the equation ... more

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; Start by writing the equation in the standard ... more

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; Start by writing the equation in the standard ... more

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; Factor the denominator on the right to find the... more

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; Factor the denominator on the right to find the... more

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Two triangles: , , & , , ; Draw a picture that ... more

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One triangle: , , ; One triangle: , , ; The sides ... more

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The length is ft and the width is ft. ; Define the... more

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The length is cm and the width is cm. ; Define the... more

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m by m ; Define the variable of interest. ; Since ... more

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The radius must be ft ; Start with a square, the ... more

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The length is ft and the width is ft. ; Define the... more

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The length is ft and the width is ft. ; Define the... more

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Length = cm, Width = cm, Height = cm ; Define the ... more

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Length = cm, Widthcm, Height = cm ; Define the ... more

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Width = ft ; Define the variable of interest. ... more

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Width = ft ; Define the variable of interest. ... more

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Width =  ft ; Define the variable of interest. ... more

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Width = ft, Length = ft, Height = ft ; Define the ... more

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Area #1 = ; Area #2 = ; The first area is larger... more

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Area #1 ; Area #2 ; The first area is larger. ; ... more

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; Read through the prompt to find values of ... more

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; Read through the prompt to find values of ... more

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hours  ; Read through the prompt to find values ... more

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people ; Define the variable of interest. Organize... more

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integers ; For a sum of , set the equation equal ... more

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sides; No,  is not possible. ; The sum is . Set ... more

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For any quadratic equation , the roots are  and... more

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For any quadratic equation , the roots are  and . ... more

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; With the equation in standard form , find a, b... more

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; With the equation in standard form , find a, b... more

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For any quadratic equation , the real solutions ... more

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For any quadratic equation , the real solutions ... more

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Only (b) are equivalent statements. ; For , the ... more

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Factoring, completing the square, and the ... more

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The discriminant determines the number and type of... more

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has two distinct real solutions, has no real ... more

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The latin word 'quadratum' is translated to '... more

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Integers: ; Rational numbers: ; Integers are the ... more

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Real numbers can be viewed as points on a number ... more

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; Multiply the top and bottom by the conjugate of... more

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A complex number is any number that can be written... more

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  ; Collect real and imaginary parts. ; Simplify... more

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; Distribute. ; Simplify. ; Evaluate the power of... more

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; Evaluate the power of . (Remember ). ; Simplify... more

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; Simplify the negative in the square root as an ... more

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; Simplify the negative in the square root as an ... more

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; Simplify the negative in the square root as an ... more

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; Simplify the negative in the square root as an ... more

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; With the equation written in standard form find... more

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; With the equation written in standard form find... more

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; With the equation written in standard form find... more

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Two complex number solutions. ; With the equation ... more

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Two real number solutions. ; With the equation in ... more

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One real number solution (double root). ; With the... more

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One real number solution (double root). ; With the... more

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 Thus,  .  ; Substitute in for . ; Find the first... more

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For and ,  and  Thus, . ; Start with the left ... more

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and . ; To add complex numbers, just add the real... more

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 Width= feet; Length= feet ;   Define the variable... more

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The graph of the given inequality starts from to ... more

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The absolute value of a number is the distance of ... more

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; The notation consists of all elements that ... more

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Negative ; Let and be any real number and be ... more

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closed interval ; Closed intervals, , are denoted ... more

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; The notation means that the distance of a ... more

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; Let be any number. The notation represents ... more

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The addition property of inequalities states that ... more

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In an inequality, the direction of the inequality ... more

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In an inequality, the direction of the inequality ... more

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Since the absolute value of a number is the ... more

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The inequality , in interval notation, is ... more

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; Find the left and right endpoints of the graph ... more

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; Find the left and right endpoints of the graph ... more

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; Find the left and right endpoints of the graph ... more

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; Find the left and right endpoints of the graph ... more

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; Find the left and right endpoints of the graph ... more

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; Find the left and right endpoints of the graph ... more

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Translate the inequality into interval notation. ... more

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Translate the inequality into interval notation. ... more

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Translate the inequality into interval notation. ... more

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Translate the inequality into interval notation. ... more

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Translate the inequality into interval notation. ... more

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Translate the inequality into interval notation. ... more

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Translate the inequality into interval notation. ... more

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Translate the inequality into interval notation. ... more

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Translate the interval notation into an inequality... more

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Translate the interval notation into an inequality... more

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Translate the interval notation into an inequality... more

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Translate the interval notation into an inequality... more

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Translate the interval notation into an inequality... more

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Translate the interval notation into an inequality... more

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Translate the interval notation into an inequality... more

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Translate the interval notation into an inequality... more

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; Subtracting on both sides of the inequality ... more

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; Adding to both sides of the inequality does ... more

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; Adding to both sides of the inequality does ... more

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; Subtracting from both sides of the inequality ... more

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; Multiplying by on both sides of the inequality... more

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; Multiplying by on both sides of the inequality... more

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;  Multiplying by on both sides of the ... more

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;  Multiplying by on both sides of the ... more

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; To obtain on one side of the inequality, ... more

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; To obtain on one side of the inequality, ... more

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  ; Multiplying by on both sides of the ... more

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;  Multiplying by on both sides of the ... more

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; Isolate on one side of the inequality.Add 7 on... more

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; Isolate on one side of the inequality.Subtract... more

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; Isolate on one side of the inequality.Subtract... more

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; Isolate on one side of the inequality.Subtract... more

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; Isolate on one side of the inequality.Add 1 ... more

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; Isolate on one side of the inequality.Add 2 ... more

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; Isolate on one side of the inequality.Expand ... more

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; Isolate on one side of the inequality.Expand ... more

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; Isolate on one side of the inequality.Expand ... more

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; Isolate on one side of the inequality.Expand ... more

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; Isolate on one side of the inequality.... more

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; Isolate on one side of the inequality.... more

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; Isolate in the middle.Add 6 on all parts.... more

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; Isolate in the middle.Subtract 2 from all ... more

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; Isolate in the middle.Subtract 4 from all ... more

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; Isolate in the middle.Subtract 3 from all ... more

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; Isolate in the middle.Eliminate the fraction ... more

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  ; Isolate in the middle.Eliminate the fraction ... more

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; Isolate in the middle.Eliminate the fraction ... more

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; Isolate in the middle.Eliminate the fraction ... more

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; Isolate on one side.Multiply the binomial ... more

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; Isolate on one side.Multiply the binomial ... more

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; Rewrite the inequality without absolute-value ... more

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; Rewrite the inequality without absolute-value ... more

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; Rewrite the inequality without absolute-value ... more

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; Rewrite the inequality without absolute-value ... more

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; Rewrite the inequality without absolute-value ... more

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; Rewrite the inequality without absolute-value ... more

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; Rewrite the inequality.Isolate the absolute ... more

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; Rewrite the inequality.Isolate the absolute ... more

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; Rewrite the inequality without absolute-value ... more

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; Rewrite the inequality without absolute-value ... more

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  ; Rewrite the inequality without absolute value ... more

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; Rewrite the inequality without absolute value ... more

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; Rewrite the inequality without absolute value ... more

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; Rewrite the inequality without absolute value ... more

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no solution ; The absolute value of any number is ... more

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; Rewrite the inequality without absolute-value ... more

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; Isolate on one side of the inequality.Subtract... more

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; Isolate on one side of the inequality.Subtract... more

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; Rewrite the inequality with no absolute value ... more

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; Rewrite the inequality without absolute value ... more

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; Solve the inequality.Isolate on one side of ... more

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; Isolate on one side of the inequality.... more

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; Solve the inequality by isolating in the ... more

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; Solve the inequality by isolating in the ... more

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; Isolate on one side of the inequality.Expand ... more

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; Isolate on one side of the inequality.Expand ... more

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; Rewrite the inequality without absolute value ... more

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; Rewrite the inequality without absolute value ... more

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; Isolate in the middle.Subtract 5 from all ... more

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; Isolate in the middle.Simplify the middle part... more

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; Rewrite the inequality without the absolute ... more

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; Rewrite the inequality without absolute value ... more

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; Since cannot be isolated in the middle, write ... more

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; Since cannot be isolated in the middle, write ... more

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; Since cannot be isolated in the middle, write ... more

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; Since cannot be isolated in the middle, write ... more

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; Write the inequality satisfying the conditions... more

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; Write the inequality satisfying the conditions... more

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; Write the inequality satisfying the conditions... more

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; Write the inequality satisfying the conditions... more

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; Translating the first half of the statement ... more

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; Translating the first half of the statement ... more

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; Write the inequality satisfying the conditions... more

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; Write the inequality satisfying the conditions... more

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; Since , just take the compound inequality for ... more

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which is between and . ;  Since , just make the ... more

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; Since , just make the compound inequality for ... more

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; If is withheld for wages, then since , just ... more

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; The total completed so far has been . If the ... more

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; Since and ranged between and , a compound ... more

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; Since by translating the prompt, and ranged ... more

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; Since and ranges between and , a compound ... more

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; The prompt can be translated into an inequality... more

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Either cal or g ; The prompt can be translated ... more

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; Write the inequality satisfying the conditions... more

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; Start with the given inequality. Show the left ... more

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is equidistant to and . ; Find the distance ... more

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; Start with the given inequality. Show the left ... more

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; Start with the given inequality. Take the ... more

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; Start with the given inequality. Show the right... more

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; Find the expression for in terms of and , ... more

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  has no solution; has one solution. ; Since a ... more

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Start with a simple inequality and multiply by a ... more

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is always a nonnegative value. ; After ... more

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Inequality notation is preferable when the ... more

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;   ; Write the solution as a set. ; more

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  ; Solve the equation by isolating . ; Write the ... more

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; Clear the equation of fractions by multiplying ... more

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; Simplify the equation into a linear equation. (... more

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No solution; ; Simplify the quadratic equation ... more

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; Clear the equation of fractions by multiplying ... more

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; Simplify the quadratic equation into standard ... more

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; Simplify the quadratic equation into standard ... more

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; With the radical expression isolated, remove ... more

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No real solutions; ; Simplify the quadratic ... more

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no real solution ; Since the trinomial is not ... more

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; To get the equation in standard quadratic form... more

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; Isolate the radical expression, then remove the... more

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; With the radical expression isolated, remove ... more

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; With one of the radical expressions isolated, ... more

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; Isolate the term with the rational exponent and... more

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; To get the equation in standard quadratic form... more

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; To get the equation in standard quadratic form... more

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; With the equation in standard quadratic form , ... more

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  ; Isolate one of the radical expressions and ... more

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; With the absolute value expression isolated, ... more

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; Isolate the absolute value expression. Then, ... more

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; Move the terms to the left side and factor out ... more

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; Solve the equation by factoring. With four ... more

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; Start by eliminating the fractions.Factor the ... more

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; Apply the square root property. ; Solve for... more

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; Let be equal to the left side of the equation.... more

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; Collect all terms on one side of the equation.... more

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Solve the inequality for .   ; Translate the ... more

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or ; Solve the compound inequality for . ; ... more

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or ; Solve the compound inequality for .(Remember... more

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or ; Express the absolute value inequality as a ... more

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or ; Express the absolute value inequality as a ... more

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or ;  Isolate the absolute value on the left side... more

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or ;  Isolate the absolute value on the left side... more

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; Subtract the real and imaginary parts, then ... more

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  ; Add the real and imaginary parts, then ... more

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  ;  Multiply the numerator and denominator by the... more

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  ; Rewrite the power of as the nearest multiple ... more

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; Expand the product using the special product ... more

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; Solve the equation using the quadratic formula... more

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  ; Solve the equation using the quadratic formula... more

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; Write the quadratic equation in standard form... more

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; Write the equation in standard form.Expand the ... more

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Find some points  that satisfy the equation.  ; ... more

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; The points of intersection of the curve and the... more

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Start by solving for in terms of .Isolate the -... more

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Find some points that satisfy the equation.  ; ... more

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Start by solving for in terms of .Isolate the -... more

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A triangle is isosceles if it has two equal sides... more

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; Write an equation in terms of using the ... more

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; Translate the sentence into an algebraic ... more

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; The simple interest is given by where is the... more

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  in A's; in CD's. ; Define the variable of ... more

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   ft. ;   Define the variable of interest. ; Let... more

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Between m and m. ; Translate the prompt into a ... more

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miles. ; Translate the prompt into a compound ... more

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  hours (about hour minutes). ; Define the ... more

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18.75 seconds37.5 seconds ; Summarize the given ... more

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days. ;   Define the variable of interest.  ; Let... more

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lb lb ; Summarize the given information in table ... more

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ounces.  ; Define the variable of interest.  ;   ... more

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Width= inches; Length= inches. ;  Define the ... more

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  feet.  ;  Define the variable of interest. ; Let... more

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2 hours ; Summarize the given information using a ... more

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6.47 feet ; Substitute into the formula. Write ... more

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36 ; Summarize the given information using a table... more

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; Since the given equation is quadratic, start by... more

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; Eliminate the radical. Make sure that the ... more

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; Start by eliminating the fractions.Multiply ... more

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; The given equation is linear. Solve the ... more

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; Since the equation involves an absolute value, ... more

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; Start by collecting all terms on one side of ... more

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; Since the expression on the left is not ... more

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; Since the equation is quadratic, write it in ... more

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Start by solving for in terms of . ; Find points... more

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Find points that satisfy the equation.  ; ... more

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; Let be equal to the left side of the equation... more

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; Let be equal to the left side of the equation... more

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; Collect all terms on one side of the equation. ... more

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; Start by eliminating the fraction.Multiply both... more

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; Start by removing the absolute-value bars.... more

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; Solve the inequality by isolating in the ... more

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; Start by removing the absolute-value bars.Use ... more

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; Apply the distributive property of ... more

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; Apply the distributive property.Combine similar... more

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; Eliminate from the denominator.Multiply the ... more

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;  Solve the equation using the quadratic formula... more

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204.63 minutes ; Summarize the given information ... more

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23.75 lb ; Summarize the given information in a ... more

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; Let be the discounted price of the product. ... more

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; Start by identifying the given values.  ; Use ... more

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