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: 72

Answer

$b=-\dfrac{3}{2}$

Work Step by Step

Using the properties of equality, the solution to the given equation, $ 3b-2=7b+4 $, is \begin{array}{l} 3b-7b=4+2 \\\\ -4b=6 \\\\ b=\dfrac{6}{-4} \\\\ b=-\dfrac{3}{2} .\end{array} CHECKING: \begin{array}{l} 3\left( -\dfrac{3}{2} \right)-2=7\left( -\dfrac{3}{2} \right)+4 \\\\ -\dfrac{9}{2}-2=-\dfrac{21}{2}+4 \\\\ -\dfrac{9}{2}-\dfrac{4}{2}=-\dfrac{21}{2}+\dfrac{8}{2} \\\\ -\dfrac{13}{2}=-\dfrac{13}{2} \text{ (TRUE)} .\end{array} Hence, the solution is $ b=-\dfrac{3}{2} $.
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