Question

which number line represents the solution set for the inequality -4(x + 3) ≤ -2 - 2x?

Explanation:

Step1: Expand the left - hand side

$-4(x + 3)=-4x-12$, so the inequality becomes $-4x-12\leq - 2-2x$.

Step2: Add $4x$ to both sides

$-4x + 4x-12\leq - 2-2x+4x$, which simplifies to $-12\leq - 2 + 2x$.

Step3: Add 2 to both sides

$-12 + 2\leq - 2+2 + 2x$, resulting in $-10\leq 2x$.

Step4: Divide both sides by 2

$\frac{-10}{2}\leq\frac{2x}{2}$, so $x\geq - 5$.

Answer:

The number line with a closed - circle at $-5$ and an arrow pointing to the right (the first option in the image where the blue line starts at $-5$ and goes to the right) represents the solution set.