Question

-2|x + 7|+11 > 5
solutions on the number line:
interval notation:
set builder notation:

Explanation:

Step1: Isolate the absolute - value term

Subtract 11 from both sides of the inequality $-2|x + 7|+11>5$.
$-2|x + 7|+11-11>5 - 11$
$-2|x + 7|>-6$

Step2: Solve for the absolute - value term

Divide both sides by - 2. Remember to reverse the inequality sign when dividing by a negative number.
$\frac{-2|x + 7|}{-2}<\frac{-6}{-2}$
$|x + 7|<3$

Step3: Rewrite the absolute - value inequality as a compound inequality

$-3

Step4: Solve the compound inequality

Subtract 7 from all parts of the compound inequality.
$-3-7$-10

Answer:

Solutions on the number line: Open - circle at - 10 and - 4, and the line segment between them.
Interval Notation: $(-10,-4)$
Set - builder Notation: $\{x|-10 < x<-4\}$