Question

solve the inequality. then graph the solution set and write it in interval notation. |2x + 2| ≥ 10 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution set is \\(\square\\) (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 \\{\square\\} (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 a b. graph b c. graph c d. graph d

Explanation:

Step1: Rewrite absolute value inequality

$$-10 \leq 2x + 2 \leq 10$$

Step2: Subtract 2 from all parts

$$-10 - 2 \leq 2x \leq 10 - 2$$
$$-12 \leq 2x \leq 8$$

Step3: Divide all parts by 2

$$\frac{-12}{2} \leq x \leq \frac{8}{2}$$
$$-6 \leq x \leq 4$$

Step4: Convert to interval notation

$$[-6, 4]$$

Answer:

A. The solution set is $[-6, 4]$.
C. (the graph with closed brackets at -6 and 4, spanning the interval between them)