Question

which number line represents the solution set for the inequality $-\frac{1}{2}x\geq4$?

Explanation:

Step1: Solve the inequality

Multiply both sides of \(-\frac{1}{2}x\geq4\) by \(- 2\). When multiplying or dividing an inequality by a negative number, the direction of the inequality sign changes. So we get \(x\leq - 8\).

Step2: Analyze the number - line representation

A closed circle at \(x = - 8\) (because the inequality is \(\leq\), including the value \(x=-8\)) and the line extending to the left (since \(x\) is less than or equal to \(-8\)).

Answer:

The number - line with a closed circle at \(-8\) and the line extending to the left.