Question

graph the solution to the inequality on the number line. |2u + 11| ≤ 3

Explanation:

Step1: Remove the absolute value

$$-3\leq2u + 11\leq3$$

Step2: Subtract 11 from all parts

$$-3-11\leq2u+11 - 11\leq3 - 11$$
$$-14\leq2u\leq-8$$

Step3: Divide all parts by 2

$$\frac{-14}{2}\leq\frac{2u}{2}\leq\frac{-8}{2}$$
$$-7\leq u\leq-4$$

Answer:

The solution is \(u\in[-7,-4]\). On the number line, we draw a solid circle at \(-7\) and \(-4\) (because the inequality includes equality) and shade the region between them.