Solve for u.

Question

–
5≤
u+34
2
≤29
Write your answer as a compound inequality with integers, proper fractions, and improper fractions in simplest form.

Answer 1

To solve the compound inequality $-5\le \frac{u+34}{2}\le 29$, we will break it into two parts and solve each part step by step.

1. Start with the left part of the compound inequality: $$-5\le \frac{u+34}{2}$$ Multiply both sides by 2: $$-10\le u+34$$ Now, subtract 34 from both sides: $$-10-34\le u$$ Simplifying gives: $$-44\le u\text{or}u\ge -44$$

2. Now, consider the right part of the compound inequality: $$\frac{u+34}{2}\le 29$$ Again, multiply both sides by 2: $$u+34\le 58$$ Subtract 34 from both sides: $$u\le 58-34$$ This simplifies to: $$u\le 24$$

3. Now, combine the results from both parts: $$-44\le u\le 24$$

Thus, the solution as a compound inequality is: $$-44\le u\le 24$$