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: 48


$(-\displaystyle \frac{3}{4},\infty)$ .

Work Step by Step

The idea is to isolate x on one side. Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbol remains the same). Multiplying/dividing with a negative number inverts the order (the inequality symbol changes). --- $5[3(2-3x)-2(5-x)]-6[5(x-2)-2(4x-3)] \lt 3x+19$ .... distribute inner parentheses $5 [6-9x-10+2x]-6[5x-10-8x+6] \lt 3x+19$ ... simplify within the brackets $5 [-7x-4]-6[-3x-4] \lt 3x+19$ ... distribute $-35x-20+18x+24 \lt 3x+19$ ... simplify $-17x+4 \lt 3x+19 \qquad $ ... $/-3x-4$ $-20x \lt 15\qquad $ ... $/\div(-20)$ ... (negative: change direction) $ x \gt \displaystyle \frac{15}{-20}$ $ x \gt -\displaystyle \frac{3}{4}$ The solution set is $(-\displaystyle \frac{3}{4},\infty)$ .
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