Question

graphing compound inequalities
which graph represents the inequality x ≤ -2 or x ≥ 0?

Explanation:

Step1: Analyze $x\leq - 2$

On a number - line, for $x\leq - 2$, we have a closed - circle at $x = - 2$ (because the inequality includes equality) and the line extends to the left.

Step2: Analyze $x\geq0$

On a number - line, for $x\geq0$, we have a closed - circle at $x = 0$ (because the inequality includes equality) and the line extends to the right.

Step3: Consider the 'or' condition

The solution of $x\leq - 2$ or $x\geq0$ is the combination of the two regions.

Answer:

The first graph (the one with closed - circles at $x=-2$ and $x = 0$, and the line extending to the left from $x=-2$ and to the right from $x = 0$) represents the inequality $x\leq - 2$ or $x\geq0$.