Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 1 - Expressions, Equations, and Inequalities - 1-5 Solving Inequalities - Practice and Problem-Solving Exercises - Page 38: 38


$$-4 \le x \le 6$$ Refer to the graph below.

Work Step by Step

Solve each inequality: \begin{align*} 6x &\ge -24\\\\ \frac{6x}{6} &\ge \frac{-24}{6}\\\\ x &\ge -4 \end{align*} $$\text{and}$$ \begin{align*} 5x&\le 30\\\\ \frac{5x}{5} &\le \frac{30}{5}\\\\ x&\le 6 \end{align*} Graph each inequality to obtain the one in the attached image below. Since the compound inequality involves the conjunction $\text{AND}$, then the solutions to the inequality are numbers common to both graphs, which are the numbers in the interval $-4 \le x \le 6$.
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