Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 159: 38


$\color{blue}{(-\frac{13}{4}, \frac{3}{4}]}$

Work Step by Step

Multiply $-2$ to each part. Note that since a negative number is multiplied to the inequality, the inequality symbols will be reversed. \begin{array}{ccccc} &-2(1)&\ge &-2 \cdot \dfrac{4x-5}{-2} &\gt &-2(9) \\&-2 &\ge &4x-5 &\gt &-18 \end{array} Add $5$ to each part: \begin{array}{ccccc} \\&-2+5 &\ge &4x-5+5 &\gt &-18+5 \\&3 &\ge &4x &\ge &-13 \end{array} Divide each part by $4$: \begin{array}{ccccc} \\&\frac{3}{4} &\ge &\frac{4x}{4} &\gt &\frac{-13}{4} \\&\frac{3}{4} &\ge &x &\gt &\frac{-13}{4} \end{array} This inequality is equivalent to: $-\frac{13}{4} \lt x \le \frac{3}{4}$ Thus, the solution to the given inequality is: $\color{blue}{(-\frac{13}{4}, \frac{3}{4}]}$
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