Question

solve the following inequality. then graph the solution set.
|x + 8| < 5
b. the solution set is one or two points. the solution set is
(type an integer or a fraction. use a comma to separate answers as needed.)
c. the solution set is ∅.
choose the correct graph below

Explanation:

Step1: Rewrite absolute value inequality

For $|x+8| < 6$, this translates to:
$$-6 < x+8 < 6$$

Step2: Subtract 8 from all parts

Subtract 8 to isolate $x$:
$$-6 - 8 < x < 6 - 8$$
$$-14 < x < -2$$

Answer:

The solution set is $\boldsymbol{-14 < x < -2}$ (or in set notation $\{x \mid -14 < x < -2\}$). The correct graph is option C (the graph with open circles at -14 and -2, and a line segment connecting them pointing inward between the two points).