Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 4 - Cumulative Review - Page 252: 24

Answer

$(-\infty, -3) \cup (2, +\infty)$

Work Step by Step

RECALL: $\\\\|a|\gt; b \longrightarrow a \gt b \text{ or } a \lt -b$ $\\\\$Use this definition of absolute value to have: $\\\\|2x+1| \gt 5 \color{red}\longrightarrow \color{black}2x+1 \gt 5 \text{ or } 2x+1 \lt -5$ $\\\\\\$Solve each inequality to have: $\\\\2x \gt 5-1 \text{ or } 2x \lt -5-1 \\\\2x \gt 4 \text{ or } 2x \lt -6 \\\\x \gt 2 \text{ or } x \lt -3$ $\\\\\\$Thus, the solution to the given inequality is: $\\\\(-\infty, -3) \cup (2, +\infty)$
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