Question

which inequalitys solution set is represented on the number line shown?
0 1 2 3 4 5 6 7 8 9 10
$\frac{x}{2} \leq 1$
$6x \leq 3$
$-2x \leq -4$
$4x \leq -8$

Explanation:

Step1: Analyze the number line

The number line has a filled dot at 2 and the line extends to the right, so the solution set is \( x \geq 2 \).

Step2: Solve each inequality

• For \( \frac{x}{2} \leq 1 \): Multiply both sides by 2, we get \( x \leq 2 \). Not matching.
• For \( 6x \leq 3 \): Divide both sides by 6, \( x \leq \frac{3}{6}=\frac{1}{2} \). Not matching.
• For \( -2x \leq -4 \): Divide both sides by -2 (reverse inequality), \( x \geq \frac{-4}{-2}=2 \). Matches the number line.
• For \( 4x \leq -8 \): Divide by 4, \( x \leq -2 \). Not matching.

Answer:

\( -2x \leq -4 \)