Solve for u.

Question

–
11u–2+13u≤
–
12 or
–
7u+1–u<17
Write your answer as a compound inequality with integers.

Answer 1

Let's solve each inequality step by step.

First Inequality:

\[ -11u - 2 + 13u \leq -12 \]

1. Combine like terms: \[ (13u - 11u) - 2 \leq -12 \] \[ 2u - 2 \leq -12 \]

2. Add 2 to both sides: \[ 2u \leq -12 + 2 \] \[ 2u \leq -10 \]

3. Divide by 2: \[ u \leq -5 \]

Second Inequality:

\[ -7u + 1 - u < 17 \]

1. Combine like terms: \[ -8u + 1 < 17 \]

2. Subtract 1 from both sides: \[ -8u < 17 - 1 \] \[ -8u < 16 \]

3. Divide by -8 and remember to reverse the inequality: \[ u > -2 \]

Combined Solution:

The solution to the inequalities are:

• From the first inequality: \( u \leq -5 \)
• From the second inequality: \( u > -2 \)

Final Result:

Now we combine the two results into a compound inequality: \[ u \leq -5 \quad \text{or} \quad u > -2 \]

In interval notation: \[ (-\infty, -5] \quad \text{or} \quad (-2, \infty) \]

Thus, the solution in terms of \( u \) is: \[ u \leq -5 \quad \text{or} \quad u > -2 \]