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 39PPS
To determine

Solve the given equation graphically and verify the solution algebraically.

Expert Solution & Answer
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Answer to Problem 39PPS

  x=−3

Explanation of Solution

Given:

The Equation: 19+3x=13+x

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: 19+3x=13+x

Graph the equation and verify the solution algebraically.

Rewrite the equation with 0 on the right side.

  19+3x=13+x19+3x−x=13+x−x  [ Subtract  x  from  both  sides ]19+2x=1319−13+2x=13−13         [ Subtract  13  from  both  sides ]2x+6=0

The related function is f(x) = 2x+6 to graph the function. Make a table.

    Table Graph f(x) = 2x+6
    x f(x)=2x+6 f(x) (x, f(x))
    −3 f(x)=2  ·  (−3)+6            =−6+6=0 0 ( −3 , 0)
    0 f(x) = 0 + 6 = +6 +6 (0, 6)

    The graph intersect the x- axis at −3 , so the solution is −3

    		Algebra 1, Chapter 3.2, Problem 39PPS

Verify the solution algebraically

  19+3x=13+x19+3x−x=13+x−x  [ Subtract  x  from  both  sides ]19+2x=1319−13+2x=13−13         [ Subtract  13  from  both  sides ]2x+6=02x+6−6=0−6   [ Subtract  13  from  both  sides ]2x=−62x2  =  − 62   [  Divide  each  side  by  2  ]x=−3

Solution of the equation: 19+3x=13+x is x=−3

Thus, the solution of the equation 19+3x=13+xis x=−3

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Chapter 3.2, Problem 38PPS
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Chapter 3.2, Problem 40PPS

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
Ch. 3.1 - Prob. 5ACYPCh. 3.1 - Prob. 5BCYPCh. 3.1 - Prob. 5CCYPCh. 3.1 - Prob. 1CYUCh. 3.1 - Prob. 2CYUCh. 3.1 - Prob. 3CYUCh. 3.1 - Prob. 4CYUCh. 3.1 - Prob. 5CYUCh. 3.1 - Prob. 6CYUCh. 3.1 - Prob. 7CYUCh. 3.1 - Prob. 8CYUCh. 3.1 - Prob. 9CYUCh. 3.1 - Prob. 10CYUCh. 3.1 - Prob. 11CYUCh. 3.1 - Prob. 12CYUCh. 3.1 - Prob. 13PPSCh. 3.1 - Prob. 14PPSCh. 3.1 - Prob. 15PPSCh. 3.1 - Prob. 16PPSCh. 3.1 - Prob. 17PPSCh. 3.1 - Prob. 18PPSCh. 3.1 - Prob. 19PPSCh. 3.1 - Prob. 20PPSCh. 3.1 - Prob. 21PPSCh. 3.1 - Prob. 22PPSCh. 3.1 - Prob. 23PPSCh. 3.1 - Prob. 24PPSCh. 3.1 - Prob. 25PPSCh. 3.1 - Prob. 26PPSCh. 3.1 - Prob. 27PPSCh. 3.1 - Prob. 28PPSCh. 3.1 - Prob. 29PPSCh. 3.1 - Prob. 30PPSCh. 3.1 - Prob. 31PPSCh. 3.1 - Prob. 32PPSCh. 3.1 - Prob. 33PPSCh. 3.1 - Prob. 34PPSCh. 3.1 - Prob. 36PPSCh. 3.1 - Prob. 37PPSCh. 3.1 - Prob. 38PPSCh. 3.1 - Prob. 39PPSCh. 3.1 - Prob. 40PPSCh. 3.1 - Prob. 41PPSCh. 3.1 - Prob. 42PPSCh. 3.1 - Prob. 43PPSCh. 3.1 - Prob. 44PPSCh. 3.1 - Prob. 45PPSCh. 3.1 - Prob. 46PPSCh. 3.1 - 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Prob. 15HPCh. 3.6 - Prob. 16HPCh. 3.6 - Prob. 17HPCh. 3.6 - Prob. 18HPCh. 3.6 - Prob. 1ACYPCh. 3.6 - Prob. 1BCYPCh. 3.6 - Prob. 1CCYPCh. 3.6 - Prob. 2ACYPCh. 3.6 - Prob. 2BCYPCh. 3.6 - Prob. 19STPCh. 3.6 - Prob. 20STPCh. 3.6 - Prob. 21STPCh. 3.6 - Prob. 22STPCh. 3.6 - Prob. 23SRCh. 3.6 - Prob. 24SRCh. 3.6 - Prob. 25SRCh. 3.6 - Prob. 26SRCh. 3.6 - Prob. 27SRCh. 3.6 - Prob. 28SRCh. 3.6 - Prob. 29SRCh. 3.6 - Prob. 30SCh. 3.6 - Prob. 31SCh. 3.6 - Prob. 32SCh. 3.6 - Prob. 33SCh. 3.6 - Prob. 34SCh. 3.6 - Prob. 35SCh. 3 - Prob. 1QCCh. 3 - Prob. 2QCCh. 3 - Prob. 3QCCh. 3 - Prob. 4QCCh. 3 - Prob. 5QCCh. 3 - Prob. 6QCCh. 3 - Prob. 13QCCh. 3 - Prob. 14QCCh. 3 - Prob. 15QCCh. 3 - Prob. 16QCCh. 3 - Prob. 17QCCh. 3 - Prob. 18QCCh. 3 - Prob. 19QCCh. 3 - Prob. 20QCCh. 3 - Prob. 21QCCh. 3 - Prob. 22QCCh. 3 - Prob. 23QCCh. 3 - Prob. 1MCQCh. 3 - Prob. 2MCQCh. 3 - Prob. 3MCQCh. 3 - Prob. 4MCQCh. 3 - Prob. 5MCQCh. 3 - Prob. 6MCQCh. 3 - Prob. 9MCQCh. 3 - Prob. 10MCQCh. 3 - Prob. 11MCQCh. 3 - Prob. 12MCQCh. 3 - 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