Question

solve the inequality and graph the solution.
-4(a + 5) ≥ 4
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Expand the left - hand side

$$-4(a + 5)=-4a-20$$
The inequality becomes $-4a - 20\geq4$.

Step2: Add 20 to both sides

$$-4a-20 + 20\geq4 + 20$$
$$-4a\geq24$$

Step3: Divide both sides by - 4 and reverse the inequality sign

When dividing an inequality by a negative number, the inequality sign is reversed.
$$\frac{-4a}{-4}\leq\frac{24}{-4}$$
$$a\leq - 6$$

Answer:

The solution of the inequality is $a\leq - 6$. On the number - line, we plot a closed circle at $-6$ (because the inequality includes equality, i.e., $a$ can be equal to $-6$) and draw a ray to the left of $-6$.