Question

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

Explanation:

Step1: Solve the inequality

Multiply both sides of $-\frac{1}{2}x\geq4$ by - 2. When multiplying an inequality by a negative number, the direction of the inequality sign changes. So we get $x\leq4\times(-2)$.

Step2: Calculate the right - hand side

$4\times(-2)=-8$, so $x\leq - 8$.
On a number line, this is represented by a closed circle at - 8 (because the inequality includes equality, $\leq$) and an arrow pointing to the left (towards smaller numbers).

Answer:

The number line with a closed circle at - 8 and an arrow pointing to the left.