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: 47

Answer

$(-\infty,-2)$.
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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). --- $3[3(x+5)+8x+7]+5[3(x-6)-2(3x-5)] \lt 2(4x+3)$ .... distribute inner parentheses $3 [3x+15+8x+7]+5[3x-18-6x+10] \lt 8x+6$ ... simplify within the brackets $3 [11x+22]+5[-3x-8] \lt 8x+6$ ... distribute $33x+66-15x-40 \lt 8x+6$ ... simplify $ 18x+26 \lt 8x+6 \qquad $ ... $/-8x-26$ $ 10x \lt -20 \qquad $ ... $/\div 10$ $ x \lt -2$ The solution set is $(-\infty,-2)$.
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