Chapter 1 - 1.7 - Linear Inequalities in One Variable - 1.7 Exercises - Page 137: 34

$-3\lt x\leq5$ See graph

For $$-1\leq-(x-4)$$ $$-1\leq-x+4$$ $$-1-4\leq-x+4-4$$ $$-5\leq-x$$ $$\frac{-5}{-1}\geq\frac{-x}{-1}$$ $$5\geq x$$ $$x\leq5$$ For $$-(x-4)\lt 7$$ $$-x+4\lt7$$ $$-x+4-4\lt7-4$$ $$-x\lt 3$$ $$\frac{-x}{-1}\gt\frac{3}{-1}$$ $$x\gt -3$$ Then, combining: $$x\gt-3\text{ and }x\leq5$$ $$-3\lt x\leq5$$ The graph is as shown.