Algebra 1
Algebra 1
1st Edition
ISBN: 9780078884801
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 3.2, Problem 43PPS
To determine

Solve the given equation graphically and verify the solution algebraically.

Expert Solution & Answer
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Answer to Problem 43PPS

  x=1.125

Explanation of Solution

Given:

The Equation: 3x−11=13x−8

Concept Used:

In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

Calculation:

The equation: 3x−11=13x−8

Graph the equation and verify the solution algebraically.

Rewrite the equation with 0 on the right side.

  3x−11=13x−83  ·  3x−  3  ·  11=  3  ·  13x−  3  ·  8  [ Multiply  both  sides by  3] 9x−33=x−249x−x−33=x−x−24  [ Subtract  x  from  both  sides ]8x−33=−248x−33+24=−24+24        [Add  24  to  both  sides ]8x−9=0

The related function is f(x)=8x−9 to graph the function. Make a table.

    Table Graph f(x)=8x−9
    x f(x)=8x−9 f(x) (x, f(x))
    1 f(x)=8  ·  1−9=−  1 0 (1,−1)
    0 f(x)=8  ·  0−9=−  9 −  9 (0,−9)

    The graph intersect the x- axis at 1.125 , so the solution is 1.125

    		Algebra 1, Chapter 3.2, Problem 43PPS

Verify the solution algebraically

  3x−11=13x−83  ·  3x−  3  ·  11=  3  ·  13x−  3  ·  8  [ Multiply  both  sides by  3] 9x−33=x−249x−x−33=x−x−24  [ Subtract  x  from  both  sides ]8x−33+33=−24+33   [Add  33  to  both  sides ]8x=98x8  =  98                             [  Divide  each  side  by  8  ]x=1.125

Solution of the equation: 3x−11=13x−8 is x=1.125

Thus, the solution of the equation 3x−11=13x−8is x=1.125

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Chapter 3.2, Problem 42PPS
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Chapter 3.2, Problem 46HP

Chapter 3 Solutions

Algebra 1

Ch. 3.1 - Prob. 35PPSCh. 3.1 - Prob. 58PPSCh. 3.1 - Prob. 60HPCh. 3.1 - Prob. 68STPCh. 3.1 - Prob. 1ACYPCh. 3.1 - Prob. 1BCYPCh. 3.1 - Prob. 2CYPCh. 3.1 - Prob. 3CYPCh. 3.1 - Prob. 4ACYPCh. 3.1 - Prob. 4BCYP
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