Chapter 1 - 1.7 - Linear Inequalities in One Variable - 1.7 Exercises - Page 137: 32

$-6\lt x\leq1$ See graph

For $$-9\leq-2x-7$$ $$-9+7\leq-2x-7+7$$ $$-2\leq-2x$$ $$\frac{-2}{-2}\geq\frac{-2x}{-2}$$ $$1\geq x$$ $$x\leq1$$ For $$-2x-7\lt5$$ $$-2x-7+7\lt5+7$$ $$-2x\lt12$$ $$\frac{-2x}{-2}\gt\frac{12}{-2}$$ $$x\gt-6$$ For $$x\leq1\text{ and }x\gt-6$$ $$-6\lt x\leq1$$ The graph is as shown.