Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 2 - Solving Linear Inequalities - Chapter Review - Page 96: 23

Answer

$r\lt-20 $ or $r\geq -5$ The graph is shown below.

Work Step by Step

The given inequality is $\Rightarrow \frac{r}{4}\lt -5$ or $-2r-7 \leq 3$ Solve the first inequality. $\Rightarrow \frac{r}{4}\lt -5$ Multiply each side by $4$. $\Rightarrow 4(\frac{r}{4})\lt 4(-5)$ Simplify. $\Rightarrow r\lt -20$ Solve the second inequality. $\Rightarrow -2r-7 \leq 3$ Add $7$ to each side. $\Rightarrow -2r-7+7 \leq 3+7$ Simplify. $\Rightarrow -2r\leq 10$ Divide each side by $-2$. Reverse the inequality symbol. $\Rightarrow \frac{-2r}{-2}\geq \frac{10}{-2}$ Simplify. $\Rightarrow r\geq -5$ Hence, the solution is $r\lt-20 $ or $r\geq -5$.
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