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 - 2.6 - Solving Absolute Value Inequalities - Exercises - Page 91: 18

Answer

$-6\leq v \leq 3$ The graph is shown below.

Work Step by Step

The given inequality is $\Rightarrow \frac{2}{3}|4v+6|-2\leq 10$ Add $2$ to each side. $\Rightarrow \frac{2}{3}|4v+6|-2+2\leq 10+2$ Simplify. $\Rightarrow \frac{2}{3}|4v+6|\leq 12$ Multiply each side by $\frac{3}{2}$. $\Rightarrow \frac{3}{2}\cdot \frac{2}{3}|4v+6|\leq \frac{3}{2}\cdot 12$ Simplify. $\Rightarrow |4v+6|\leq 18$ Write a compound inequality. $\Rightarrow 4v+6\leq 18$ and $4v+6\geq -18$ Subtract $6$ from each side. $\Rightarrow 4v+6-6\leq 18-6$ and $4v+6-6\geq -18-6$ Simplify. $\Rightarrow 4v\leq 12$ and $4v\geq -24$ Divide each side by $4$. $\Rightarrow \frac{4v}{4}\leq \frac{12}{4}$ and $\frac{4v}{4}\geq -\frac{24}{4}$ Simplify. $\Rightarrow v\leq 3$ and $v\geq -6$ Hence, the solution is $-6\leq v \leq 3$.
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