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: 35

Answer

The solution set is $[0, \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). --- $ 4(x+1)+2 \geq 3x+6\qquad $ ... distribute, simplify $4x+4+2 \geq 3x+6$ $ 4x+6 \geq 3x+6\qquad $ ... $/-6-3x $ $ x \geq 0$ The solution set is $[0, \infty) $.
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