Question

which number line shows the solutions to (\frac{1}{2}x - 2 > 0)?

Explanation:

Step1: Solve the inequality for \( x \)

Start with the inequality \( \frac{1}{2}x - 2 > 0 \). Add 2 to both sides:
\( \frac{1}{2}x - 2 + 2 > 0 + 2 \)
Simplify: \( \frac{1}{2}x > 2 \).

Step2: Isolate \( x \)

Multiply both sides by 2 to solve for \( x \):
\( 2 \times \frac{1}{2}x > 2 \times 2 \)
Simplify: \( x > 4 \).

Step3: Analyze the number line

The solution \( x > 4 \) means we need a number line with an open circle at 4 (since 4 is not included) and an arrow pointing to the right (for values greater than 4).

Looking at the options, the second number line (from top) has an open circle at 4 and the arrow pointing right (red part to the right of 4), which matches \( x > 4 \).

Answer:

The second number line (from top) with open circle at 4 and arrow to the right (e.g., the one with red segment starting at open circle 4 and going right).