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 41PPS
To determine

Solve the given equation graphically and verify the solution algebraically.

Expert Solution & Answer
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Answer to Problem 41PPS

  x=−2

Explanation of Solution

Given:

The Equation: 15x−30=5x−50

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: 15x−30=5x−50

Graph the equation and verify the solution algebraically.

Rewrite the equation with 0 on the right side.

  15x−30=5x−5015x−5x−30=5x−5x−50  [ Subtract  5x  from  both  sides ]10x−30=−5010x−30+50=−50+50        [ Subtract  50  from  both  sides ]10x  +20=0

The related function is f(x)=10x+20 to graph the function. Make a table.

    Table Graph f(x)=10x+20
    x f(x)=10x+20 f(x) (x, f(x))
    −2 f(x)=10· −2+20=0 0 ( −2 , 0)
    0 f(x)=10· 0+20=20 20 (0,20)

    The graph intersect the x- axis at −2 , so the solution is −2

    		Algebra 1, Chapter 3.2, Problem 41PPS

Verify the solution algebraically

  15x−30=5x−5015x−5x−30=5x−5x−50  [ Subtract  5x  from  both  sides ]10x−30=−5010x−30+30=−50+30        [ Subtract  50  from  both  sides ]10x  =−2010x10  =  −2010                             [  Divide  each  side  by  10  ]x=−2

Solution of the equation: 15x−30=5x−50 is x=−2

Thus, the solution of the equation 15x−30=5x−50is x=−2

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Chapter 3.2, Problem 40PPS
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Chapter 3 Solutions

Algebra 1

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