Chapter 1 - 1.7 - Linear Inequalities in One Variable - 1.7 Exercises - Page 137: 40

$3\lt x\lt9$ See graph

For $$-1\lt2-\frac{x}{3}$$ $$-1-2\lt2-\frac{x}{3}-2$$ $$-3\lt-\frac{x}{3}$$ $$-3(-3)\gt -\frac{x}{3}(-3)$$ $$9\gt x$$ $$x\lt 9$$ For $$2-\frac{x}{3}\lt1$$ $$2-\frac{x}{3}-2\lt1-2$$ $$-\frac{x}{3}\lt-1$$ $$-\frac{x}{3}(-3)\gt-1(-3)$$ $$x\gt3$$ Combining: $$x\gt 3\text{ and }x\lt9$$ $$3\lt x\lt9$$ The graph of the solution set is as shown.