Question

solve the compound inequality for x and identify the graph of its solution.
2x ≤ -8 or 3x + 1 > 13
choose the answer that gives both the correct solution and the correct graph.
a. solution: x ≤ -4 or x ≥ 4
graph with closed circles at -4 and 4, arrows left from -4 and right from 4

b. solution: x ≤ -4 or x > 4
graph with closed circle at -4, open circle at 4, arrow left from -4 and right from 4

c. solution: x ≥ -4 and x < 4
graph with closed circle at -4, open circle at 4, arrow left from -4 and right from 4

d. solution: x ≤ -4 or x > 4
graph with closed circle at -4, open circle at 4, arrow left from -4 and right from 4 (yellow background)

Explanation:

Step1: Solve $2x \leq -8$

Divide both sides by 2:
$\frac{2x}{2} \leq \frac{-8}{2}$
$x \leq -4$

Step2: Solve $3x + 1 > 13$

Subtract 1 from both sides:
$3x + 1 - 1 > 13 - 1$
$3x > 12$
Divide by 3:
$\frac{3x}{3} > \frac{12}{3}$
$x > 4$

Step3: Match solution to graph

For $x \leq -4$, use a closed dot at $-4$ with an arrow left. For $x > 4$, use an open dot at $4$ with an arrow right, which matches option D.

Answer:

D. Solution: $x \leq -4$ or $x > 4$