Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.8 Absolute Value Equations and Inequalities - 1.8 Exercises: 29

Answer

The solution is $(-\infty,-4]\cup[-1,\infty)$

Work Step by Step

$|2x+5|\ge3$ Solving this absolute value inequality is equivalent to solving two separate inequalities, which are: $2x+5\ge3$ and $2x+5\le-3$ $\textbf{Solve the first inequality:}$ $2x+5\ge3$ Take $5$ to the right side: $2x\ge3-5$ $2x\ge-2$ Take $2$ to divide the right side: $x\ge-\dfrac{2}{2}$ $x\ge-1$ $\textbf{Solve the second inequality:}$ $2x+5\le-3$ Take $5$ to the right side: $2x\le-3-5$ $2x\le-8$ Take $2$ to divide the right side: $x\le-\dfrac{8}{2}$ $x\le-4$ Expressing the solution in interval notation: $(-\infty,-4]\cup[-1,\infty)$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.