Chapter 1 - 1.7 - Linear Inequalities in One Variable - 1.7 Exercises - Page 137: 36

$-3\leq x\lt 7$ See graph

For $$0\leq\frac{x+3}{2}$$ $$0\leq x+3$$ $$0-3\leq x+3-3$$ $$-3\leq x$$ $$x\geq -3$$ For $$\frac{x+3}{2}\lt5$$ $$x+3\lt 10$$ $$x+3-3\lt10-3$$ $$x\lt 7$$ Combining: $$x\geq-3\text{ and }x\lt7$$ $$-3\leq x\lt 7$$ The graph is as shown.