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 - Page 95: 86



Work Step by Step

Using the properties of equality, the solution to the given equation, $ \dfrac{3}{2}(2x+5)=-\dfrac{15}{2} $, is \begin{array}{l} \dfrac{2}{3}\left[\dfrac{3}{2}(2x+5)\right]=-\dfrac{15}{2}\left[ \dfrac{2}{3}\right] \\\\ 2x+5=-5 \\\\ 2x=-5-5 \\\\ 2x=-10 \\\\ x=-\dfrac{10}{2} \\\\ x=-5 .\end{array} CHECKING: \begin{array}{l} \dfrac{3}{2}(2(-5)+5)=-\dfrac{15}{2} \\\\ \dfrac{3}{2}(-10+5)=-\dfrac{15}{2} \\\\ \dfrac{3}{2}(-5)=-\dfrac{15}{2} \\\\ -\dfrac{15}{2}=-\dfrac{15}{2} \text{ (TRUE)} .\end{array} Hence, the solution is $ x=-5 $.
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