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 \(- 2\). Remember that when multiplying or dividing an inequality by a negative number, the direction of the inequality sign changes. So we have \(x\leq4\times(-2)\), which simplifies to \(x\leq - 8\).

Step2: Analyze the number - line representation

The solution \(x\leq - 8\) means that the number line should have a closed circle at \(-8\) (because the inequality is \(\leq\), including \(-8\)) and the line should extend to the left (towards more negative numbers).

Answer:

The second number line (the one with a closed circle at \(-8\) and the line extending to the left) represents the solution set of the inequality \(-\frac{1}{2}x\geq4\).