Question

solve the inequality for u.
-2u - 16 ≤ 3u + 24
simplify your answer as much as possible.

Explanation:

Step1: Add 2u to both sides

To get all the u terms on one side, we add \(2u\) to both sides of the inequality \(-2u - 16\leq3u + 24\). This gives \(-2u+2u - 16\leq3u + 2u+ 24\), which simplifies to \(-16\leq5u + 24\).

Step2: Subtract 24 from both sides

Next, we subtract 24 from both sides to isolate the term with u. So, \(-16 - 24\leq5u+24 - 24\), which simplifies to \(-40\leq5u\).

Step3: Divide both sides by 5

Now, we divide both sides by 5 to solve for u. \(\frac{-40}{5}\leq\frac{5u}{5}\), which simplifies to \(-8\leq u\) or \(u\geq - 8\).

Answer:

\(u\geq - 8\)