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

Answer:

First, 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 get (x\leq - 8). On a number - line, this is represented by a closed circle at - 8 (because the inequality includes equality, i.e., (x) can be equal to - 8) and an arrow pointing to the left (towards smaller numbers).

Explanation:

Step1: Isolate the variable (x)

Multiply both sides of (-\frac{1}{2}x\geq4) by - 2. Since we multiply by a negative number, the inequality sign flips. We have (x\leq4\times(-2)).

Step2: Calculate the right - hand side

(4\times(-2)=-8), so (x\leq - 8).

Step3: Interpret on number line

A closed circle at - 8 and an arrow to the left represent (x\leq - 8) on the number line.