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: 54


$[\displaystyle \frac{3}{2},\frac{11}{2})$

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\leq 4x-3 \lt 19 \qquad $ ... add $3$ to all $ 6\leq 4x \lt 22 \qquad $ ... divide with $4$ $\displaystyle \frac{6}{4}\leq x \lt \frac{22}{4}$ $\displaystyle \frac{3}{2}\leq x \lt \frac{11}{2}$ ... left border included, right border excluded The solution set is $[\displaystyle \frac{3}{2},\frac{11}{2})$ .
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