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 - Mid-Chapter Review - Mixed Review: 15

Answer

$x=\dfrac{23}{7}$

Work Step by Step

Using the properties of equality, the solution to the given equation, $ \dfrac{2}{3}(x-2)-1=-\dfrac{1}{2}(x-3) $, is \begin{array}{l} 6\left[ \dfrac{2}{3}(x-2)-1 \right]=\left[ -\dfrac{1}{2}(x-3) \right]6 \\\\ 4(x-2)-6(1)=-3(x-3) \\\\ 4x-8-6=-3x+9 \\\\ 4x+3x=9+8+6 \\\\ 7x=23 \\\\ x=\dfrac{23}{7} .\end{array}
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