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

Answer:

The first number - line (the one with the arrow pointing left and ending at 0.5 with a closed - circle at 0.5)

Explanation:

Step1: Expand the right - hand side

$2x−6\geq6(x - 2)+8$ becomes $2x−6\geq6x-12 + 8$.

Step2: Simplify the right - hand side

$2x−6\geq6x - 4$.

Step3: Move x terms to one side

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

Step4: Combine like terms

$-4x\geq2$.

Step5: Solve for x

$x\leq-\frac{1}{2}=-0.5$. The solution set includes all numbers less than or equal to $-0.5$, which is represented by the first number - line.