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 R - Elementary Algebra Review - R.2 Equations, Inequalities, and Problem Solving - R.2 Exercise Set - Page 947: 54


$\left\{ t|t \ge -\dfrac{8}{33} \right\} \text{ or } \left[ -\dfrac{8}{33},\infty \right) $

Work Step by Step

Using the properties of inequality, the given inequality, $ \dfrac{2}{3}t+\dfrac{8}{9}\ge\dfrac{4}{6}-\dfrac{1}{4}t ,$ is equivalent to \begin{array}{l}\require{cancel} 36\left( \dfrac{2}{3}t+\dfrac{8}{9} \right) \ge \left(\dfrac{4}{6}-\dfrac{1}{4}t \right)36 \\\\ 12(2t)+4(8) \ge 4(6)-t(9) \\\\ 24t+32 \ge 24-9t \\\\ 24t+9t \ge 24-32 \\\\ 33t \ge -8 \\\\ t \ge -\dfrac{8}{33} .\end{array} Hence, the solution is $ \left\{ t|t \ge -\dfrac{8}{33} \right\} \text{ or } \left[ -\dfrac{8}{33},\infty \right) .$
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