Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 2 - Equations, Inequalities, and Problem Solving - 2.2 Using the Principles Together - 2.2 Exercise Set: 80

Answer

$x=-\dfrac{3}{4}$

Work Step by Step

Using the properties of equality, the solution to the given equation, $ 4x-(x+6)=5(3x-1)+8 $, is \begin{array}{l} 4x-x-6=15x-5+8 \\\\ 3x-6=15x+3 \\\\ 3x-15x=3+6 \\\\ -12x=9 \\\\ x=\dfrac{9}{-12} \\\\ x=-\dfrac{3}{4} .\end{array} CHECKING: \begin{array}{l} 4\left( -\dfrac{3}{4} \right)-\left(-\dfrac{3}{4}+6 \right)=5\left(3\left( -\dfrac{3}{4} \right)-1\right)+8 \\\\ -3-\left(-\dfrac{3}{4}+\dfrac{24}{4} \right)=5\left(-\dfrac{9}{4}-\dfrac{4}{4}\right)+8 \\\\ -3-\dfrac{21}{4}=5\left(-\dfrac{13}{4}\right)+8 \\\\ -\dfrac{12}{4}-\dfrac{21}{4}=-\dfrac{65}{4}+\dfrac{32}{4} \\\\ -\dfrac{33}{4}=-\dfrac{33}{4} \text{ (TRUE)} .\end{array} Hence, the solution is $ x=-\dfrac{3}{4} $.
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