Question

which number line represents the solution set for the inequality $-\frac{1}{2}xgeq4$?

Explanation:

Step1: Solve the inequality

Multiply both sides by - 2. When multiplying an inequality by a negative number, the direction of the inequality sign changes. So, $x\leqslant4\times(-2)$.
$x\leqslant - 8$

Step2: Interpret on number - line

The solution $x\leqslant - 8$ means all values of $x$ that are less than or equal to - 8. On a number - line, this is represented by a closed circle at - 8 (because $x$ can equal - 8) and an arrow pointing to the left.

Answer:

The second number - line (the one with a closed circle at - 8 and the arrow pointing to the left)