Question

1. solve the absolute value inequality and graph the solution set. |x + 8| < 16

Explanation:

Step1: Rewrite absolute value inequality

$-16 < x + 8 < 16$

Step2: Subtract 8 from all parts

$-16 - 8 < x + 8 - 8 < 16 - 8$

Step3: Simplify all expressions

$-24 < x < 8$

Step4: Describe graph rules

On a number line, draw open circles at $x=-24$ and $x=8$, then shade the region between the two circles.

Answer:

The solution to the inequality is $\boldsymbol{-24 < x < 8}$.
For the graph: Draw a number line, place open circles at $-24$ and $8$, and shade the interval between these two points.