Question

which number line represents the solution set for the inequality 2x - 6 ≥ 6(x - 2) + 8?

Explanation:

Step1: Expand the right - hand side

$2x - 6\geq6x-12 + 8$

Step2: Simplify the right - hand side

$2x - 6\geq6x - 4$

Step3: Move the x terms to one side

$2x-6x\geq - 4 + 6$

Step4: Combine like terms

$-4x\geq2$

Step5: Solve for x

$x\leq-\frac{2}{4}=-\frac{1}{2}=-0.5$

Answer:

The number line with a closed - circle at $-0.5$ and an arrow pointing to the left represents the solution set. So the third option (the number line with a closed - circle at $-0.5$ and arrow going left) is correct.