Question

solve the following inequality. then graph the solution set. |x + 8| < 6 a. the solution is an interval. the solution is \boxed{} (simplify your answer. type your answer in interval notation. use integers or fractions for any numbers in the expression.) b. the solution set is one or two points. the solution set is \boxed{} (type an integer or a fraction. use a comma to separate answers as needed.) c. the solution set is \varnothing. choose the correct graph below. a. graph b. graph c. graph d. graph e. graph f. graph

Explanation:

Step1: Apply absolute value rule

For $|x+8|<6$, rewrite as:
$$-6 < x+8 < 6$$

Step2: Subtract 8 from all parts

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

Step3: Identify matching graph

The interval $(-14, -2)$ corresponds to a number line with open circles at $-14$ and $-2$, and shading between them.

Answer:

A. The solution is an interval. The solution is $\boldsymbol{(-14, -2)}$
C. (the graph with open circles at -14 and -2, shading between them, option C in the image)