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: 36

Answer

The solution set is $(5, \infty)$ .
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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). Multiplying/dividing with a negative number inverts the order (the inequality symbol changes). --- $ 8x+3 \gt 3(2x+1)+x+5\qquad $ ... distribute, simplify $8x+3 \gt 6x+3+x+5$ $ 8x+3 \gt 7x+8\qquad $ ... $/-3-7x $ $8x-7x \gt >8-3$ $ x \gt 5$ The solution set is $(5, \infty)$ .
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