Question

x > 2
<---|---|---|---|---|---|---|○|---|---|--->
x ≤ 4
<---|---|---|---|---|---|---|---|---|⊖|---|--->
-4 < x ≤ 2
<---|---|---|---|---|---|---|---|---|---|--->

Explanation:

Step1: Analyze \( x > 2 \) on number line

For \( x > 2 \), the open circle at 2 (since \( > \)) and line to the right.

Step2: Analyze \( x \leq 4 \) on number line

For \( x \leq 4 \), closed circle at 4 (since \( \leq \)) and line to the left.

Step3: Analyze \( -4 < x \leq 2 \) on number line

For \( -4 < x \leq 2 \), open circle at -4 (since \( < \)) and closed circle at 2 (since \( \leq \)), line between -4 and 2. But check consistency: \( x > 2 \) and \( x \leq 4 \) intersection is \( 2 < x \leq 4 \), while \( -4 < x \leq 2 \) conflicts with \( x > 2 \). Wait, maybe the task is to graph? Wait, the problem (maybe graphing inequalities). Wait, let's correct:

Wait, the first inequality \( x > 2 \): open circle at 2, arrow right.

Second \( x \leq 4 \): closed circle at 4, arrow left.

Third \( -4 < x \leq 2 \): open at -4, closed at 2, line between. But maybe the question is to find the intersection of \( x > 2 \) and \( x \leq 4 \), which is \( 2 < x \leq 4 \). But the given \( -4 < x \leq 2 \) is inconsistent with \( x > 2 \). Maybe the problem is to graph each inequality:

For \( x > 2 \): number line with open circle at 2, shading right.

For \( x \leq 4 \): closed circle at 4, shading left.

For \( -4 < x \leq 2 \): open at -4, closed at 2, shading between -4 and 2.

But maybe the question is to identify the correct graph or solve the compound inequality. Wait, the original problem (as per image) has three inequalities with their number lines. Maybe the task is to graph them correctly. Let's re-express:

1. \( x > 2 \): Open circle at 2 (since not equal), draw line to the right.

1. \( x \leq 4 \): Closed circle at 4 (since equal), draw line to the left.

1. \( -4 < x \leq 2 \): Open circle at -4 (since \( < \)), closed circle at 2 (since \( \leq \)), draw line between -4 and 2.

But if we consider the intersection of \( x > 2 \) and \( x \leq 4 \), it's \( 2 < x \leq 4 \), which would have open at 2, closed at 4, line between.

Answer:

To graph the inequalities:

• \( \boldsymbol{x > 2} \): Open circle at \( 2 \), shade to the right.
• \( \boldsymbol{x \leq 4} \): Closed circle at \( 4 \), shade to the left.
• \( \boldsymbol{-4 < x \leq 2} \): Open circle at \( -4 \), closed circle at \( 2 \), shade between \( -4 \) and \( 2 \).

(If finding the intersection of \( x > 2 \) and \( x \leq 4 \), the solution is \( \boldsymbol{2 < x \leq 4} \), graphed with open circle at \( 2 \), closed circle at \( 4 \), shaded between.)