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: 28

Answer

$-\frac{7}{3}\lt g \lt 1$ The graph is shown below.

Work Step by Step

The given inequality is $\Rightarrow |-3g-2|+1\lt 6$ Subtract $1$ from each side. $\Rightarrow |-3g-2|+1-1\lt 6-1$ Simplify. $\Rightarrow |-3g-2|\lt 5$ Write a compound inequality. $\Rightarrow -3g-2\lt 5$ and $-3g-2\gt -5$ Add $2$ to each side. $\Rightarrow -3g-2+2\lt 5+2$ and $-3g-2+2\gt -5+2$ Simplify. $\Rightarrow -3g\lt 7$ and $-3g\gt -3$ Divide each side by $-3$. Reverse the inequality symbol. $\Rightarrow \frac{-3g}{-3}\gt \frac{7}{-3}$ and $\frac{-3g}{-3}\lt \frac{-3}{-3}$ Simplify. $\Rightarrow g\gt -\frac{7}{3}$ and $g\lt 1$ Hence, the solution is $-\frac{7}{3}\lt g \lt 1$.
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