Chapter 1 - 1.7 - Linear Inequalities in One Variable - 1.7 Exercises - Page 137: 37

$-5\leq x\lt 1$ See graph

For $$-1\lt \frac{-x-2}{3}$$ $$-3\lt -x-2$$ $$-3+2\lt-x-2+2$$ $$-1\lt-x$$ $$\frac{-1}{-1}\gt\frac{-x}{-1}$$ $$x\gt x$$ $$x\lt 1$$ For $$\frac{-x-2}{3}\leq1$$ $$-x-2\leq3$$ $$-x-2+2\leq3+2$$ $$-x\leq5$$ $$\frac{-x}{-1}\geq\frac{5}{-1}$$ $$x\geq -5$$ Combining: $$x\geq-5\text{ and }x\lt1$$ $$-5\leq x\lt 1$$ The graph is as shown.