Question

which number line represents the solution set for the inequality -\frac{1}{2}x \geq 4?

Explanation:

Step1: Solve the inequality \(-\frac{1}{2}x\geq4\)

Multiply both sides 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

On a number - line, the solution \(x\leq - 8\) is represented by a closed circle at - 8 (because the inequality includes equality, i.e., \(\geq\) becomes \(\leq\) after multiplying by a negative number) and an arrow pointing to the left.

Answer:

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