Precalculus (6th Edition)

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

Chapter 1 - Equations and Inequalities - 1.7 Inequalities - 1.7 Exercises - Page 159: 17


$\color{blue}{(-\infty, +\infty)}$

Work Step by Step

Distribute $3$ to obtain: $3(x) + 3(5)+1 \ge 5+3x \\3x+15+1 \ge 5+3x \\3x+16 \ge 5+3x$ Subtract $16$ and $3x$ to both sides, then combine like terms to obtain: $3x+16-16-3x\ge 5+3x-16-3x \\0\ge -11$ The resulting statement above is true, which means that any real numbers is a solution. Thus , the solution set is: $\color{blue}{(-\infty, +\infty)}$
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