Question

1. graph the solution of the inequality -3(x + 1) ≤ 6 on the number line.

Explanation:

Step1: Expand the left - hand side

$-3(x + 1)=-3x-3$, so the inequality becomes $-3x - 3\leq6$.

Step2: Add 3 to both sides

$-3x-3 + 3\leq6 + 3$, which simplifies to $-3x\leq9$.

Step3: Divide both sides by - 3 and reverse the inequality sign

Since we are dividing by a negative number, the inequality sign flips. So $\frac{-3x}{-3}\geq\frac{9}{-3}$, resulting in $x\geq - 3$.

Answer:

The correct graph is the one with a closed - circle at $-3$ and an arrow pointing to the right. So the second option (the one with a red - circle at $-3$ and an arrow going to the right).