Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.9 - Linear Inequalities and Absolute Value Inequalities - Exercise Set - Page 138: 55

Answer

$[3, 6)$

Work Step by Step

The idea is to isolate $x$ in the middle. Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbols remain). Multiplying/dividing with a negative number inverts the order (the inequality symbols changes). --- $-3\displaystyle \leq\frac{2}{3}x-5 \lt -1 \qquad $ ... all parts $\times 3$ $-9\leq 2x-15 \lt -3 \qquad $ ... add $15$ to all parts $ 6 \leq 2x \lt 12 \qquad $ ... divide all by 2 $3 \leq x \lt 6 $ ... left border included, right border excluded The solution set is $[3, 6)$ .
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