Question

solve the inequality. graph the solution.\\(|2x + 4| - 15 \leq -3\\)\\(\\ \\)\\(\\ \\)select the correct choice below and, if necessary, fill in the answer box to complete your choice.\\(\bigcirc\\) a. the solution is \\(\square\\).\\(\\ \\)\\(\\ \\) (type an inequality or a compound inequality. use integers or fractions for any numbers in the expression.)\\(\bigcirc\\) b. the solution is all real numbers.\\(\bigcirc\\) c. there is no solution.\\(\\ \\)choose the correct graph below.\\(\bigcirc\\) a. \\(\bigcirc\\) b. \\(\bigcirc\\) c. \\(\bigcirc\\) d. \\(\bigcirc\\) e. \\(\bigcirc\\) f. the graph contains no points.

Explanation:

Step1: Isolate the absolute value

Add 15 to both sides.
$$|2x+4| - 15 + 15 \leq -3 + 15$$
$$|2x+4| \leq 12$$

Step2: Rewrite without absolute value

Convert to compound inequality.
$$-12 \leq 2x+4 \leq 12$$

Step3: Subtract 4 from all parts

Isolate the term with $x$.
$$-12 - 4 \leq 2x+4 - 4 \leq 12 - 4$$
$$-16 \leq 2x \leq 8$$

Step4: Divide all parts by 2

Solve for $x$.
$$\frac{-16}{2} \leq \frac{2x}{2} \leq \frac{8}{2}$$
$$-8 \leq x \leq 4$$

Answer:

For the first part:
A. The solution is $\boldsymbol{-8 \leq x \leq 4}$.

For the graph part:
C. (The graph with closed dots at -8 and 4, shading between them, which matches the number line option C shown)