Question

graph the compound inequality on the number line. x≤0 and x≥ - 4

Explanation:

Step1: Identify the lower - bound

The inequality $x\geq - 4$ means $x$ can be equal to - 4 or any number greater than - 4. On the number line, we use a closed - circle at $x=-4$ (since the inequality includes equality).

Step2: Identify the upper - bound

The inequality $x\leq0$ means $x$ can be equal to 0 or any number less than 0. On the number line, we use a closed - circle at $x = 0$ (since the inequality includes equality).

Step3: Shade the interval

We shade the region on the number line that satisfies both inequalities. The region between $x=-4$ and $x = 0$ (including both endpoints) is the solution set.

Answer:

On the number line, place a closed - circle at $x=-4$ and a closed - circle at $x = 0$, then shade the region between them.