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: 37

Answer

$\color{blue}{[-\frac{16}{3}, \frac{19}{3}]}$

Work Step by Step

Multiply $-5$ to each part. Note that since a negative number is multiplied to the inequality, the inequality symbols will be reversed. \begin{array}{ccccc} &-5(-3)&\ge &-5 \cdot \dfrac{3x-4}{-5} &\ge &-5(4) \\&15 &\ge &3x-4 &\ge &-20 \end{array} Add $4$ to each part: \begin{array}{ccccc} \\&15+4 &\ge &3x-4+4 &\ge &-20+4 \\&19 &\ge &3x &\ge &-16 \end{array} Divide each part by $3$: \begin{array}{ccccc} \\&\frac{19}{3} &\ge &\frac{3x}{3} &\ge &\frac{-16}{3} \\&\frac{19}{3} &\ge &x &\ge &\frac{-16}{3} \end{array} This inequality is equivalent to: $-\frac{16}{3} \le x \le \frac{19}{3}$ Thus, the solution to the given inequality is: $\color{blue}{[-\frac{16}{3}, \frac{19}{3}]}$
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