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 \(-5 \leq \frac{u + 34}{2} \leq 29\), we will break it into two parts and solve each part step by step.

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

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

3. Now, combine the results from both parts: \[ -44 \leq u \leq 24 \]

Thus, the solution as a compound inequality is: \[ -44 \leq u \leq 24 \]