Question

which of the following graphs represents the solution to the inequality?
an inequality is shown below.

$-2 < 2x + 6 \leq 12$

which of the following graphs represents the solution to the inequality?

(graphs are shown with number lines from -6 to 6, with different open and closed dots and line segments.)

Explanation:

Step1: Solve the left inequality

Subtract 6 from all parts: $-2 - 6 < 2x + 6 - 6 \leq 12 - 6$
Simplify: $-8 < 2x \leq 6$

Step2: Divide by 2

Divide each part by 2: $\frac{-8}{2} < \frac{2x}{2} \leq \frac{6}{2}$
Simplify: $-4 < x \leq 3$

Step3: Analyze the number line

• Open circle at $-4$ (since $x > -4$, not equal)
• Closed circle at $3$ (since $x \leq 3$, equal)
• Line between $-4$ (open) and $3$ (closed).

Check the options: The second option has an open circle at $-4$ and closed at $3$, with the line in between.

Answer:

The second graph (the one with open circle at -4, closed at 3, and line between them)