Question

Write a compound inequality that can be used to solve the absolute value inequality

|u + 5| < 19.

Solve the compound inequality.

Graph the solution.

Answer 1

`\large\boxed{u<14\ and\ u>-24\to-24<u<14\to u\in(-24,\ 14)}`

Explanation:

`|x|<a\Rightarrow x < a\ and\ x>-a\\\\|x|>a\Rightarrow x>a\ or\ x<-a\\==============================\\\\|u+5|<19\Rightarrow u+5<19\ and\ u+5>-19\qquad\text{subtract 5 from both sides}\\\\u<14\ and\ u>-24\to-24<u<14\to u\in(-24,\ 14)`