which number line represents the solution set for the inequality $-\\frac{1}{2}x\\geq4$?
which number line represents the solution set for the inequality $-\\frac{1}{2}x\\geq4$?
Answer
Explanation:
Step1: Solve the inequality
Multiply both sides of the inequality (-\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 have (x\leq4\times(-2)), which simplifies to (x\leq - 8).
Step2: Analyze the number - line representation
A number - line representation of (x\leq - 8) has a closed circle at (-8) (because the inequality includes equality, i.e., (x=-8) is part of the solution set) and the line extends to the left (towards more negative numbers).
Answer:
The number - line with a closed circle at (-8) and the line extending to the left (the second option among the given ones) represents the solution set of the inequality (-\frac{1}{2}x\geq4).