Chapter 1 - 1.7 - Linear Inequalities in One Variable - 1.7 Exercises - Page 137: 53

$x\leq-5\text{ or }x\geq11$ See graph

Apply absolute rule: If $|u|\geq a,~a\gt 0$, then $u\leq-a\text{ or }u\geq a$. Take $u=\frac{x-3}{2}$ and $a=4$. $$\frac{x-3}{2}\leq-4\text{ or }\frac{x-3}{2}\geq4$$ $$x-3\leq-8\text{ or }x-3\geq8$$ $$x-3+3\leq-8+3\text{ or }x-3+3\geq8+3$$ $$x\leq-5\text{ or }x\geq11$$ The graph of the solution set is as shown.