Chapter 1 - 1.7 - Linear Inequalities in One Variable - 1.7 Exercises - Page 137: 56

$x\lt-28\text{ or }x\gt0$ See graph

$$|x+14|+3\gt17$$ $$|x+14|+3-3\gt17-3$$ $$|x+14|\gt14$$ Apply absolute rule: If $|u|\gt a,~a\gt 0$, then $u\lt-a\text{ or }u\gt a$. Take $u=x+14$ and $a=14$. $$x+14\lt-14\text{ or }x+14\gt14$$ $$x+14-14\lt-14-14\text{ or }x+14-14\gt14-14$$ $$x\lt-28\text{ or }x\gt0$$ The graph of the solution set is as shown.