Question

which number line represents the solution set for the inequality - 1/2 x ≥ 4?

Explanation:

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

Multiply both sides by - 2. When multiplying an inequality by a negative number, the direction of the inequality sign changes. So we have \(x\leq - 8\).

Step2: Analyze the number - line representations

A closed - circle is used for \(\leq\) or \(\geq\), and an open - circle is used for \(<\) or \(>\). The solution \(x\leq - 8\) is represented by a closed - circle at \(x = - 8\) 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.