Question

solve the inequality and graph the solution. - 12 ≥ 6(u + 6) to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.

Explanation:

Step1: Expand the right - hand side

$$-12\geq6(u + 6)$$
$$-12\geq6u+36$$

Step2: Subtract 36 from both sides

$$-12-36\geq6u+36 - 36$$
$$-48\geq6u$$

Step3: Divide both sides by 6

$$\frac{-48}{6}\geq\frac{6u}{6}$$
$$- 8\geq u$$ or $$u\leq - 8$$

To graph \(u\leq - 8\):

• The endpoint is \(u=-8\). Since the inequality is \(\leq\) (closed), we use a closed circle at \(u =-8\).
• The ray goes to the left (because \(u\) is less than or equal to \(-8\))

Answer:

The solution of the inequality is \(u\leq - 8\). On the number - line, we have a closed circle at \(-8\) and a ray extending to the left.