Let's solve the inequality:

\[
-32 - 4u + 5 < -13
\]

### Step 1: Combine like terms on the left-hand side.
\[
-32 + 5 - 4u < -13
\]
\[
-27 - 4u < -13
\]

### Step 2: Add 27 to both sides to isolate the term with \( u \).
\[
-4u < -13 + 27
\]
\[
-4u < 14
\]

### Step 3: Divide both sides by \( -4 \), and since we are dividing by a negative number, we must reverse the inequality sign.
\[
u > \frac{14}{-4}
\]
\[
u > -\frac{7}{2}
\]

So the solution is:
\[
u > -\frac{7}{2} \quad \text{or} \quad u > -3.5
\]

Would you like more details on any part of the solution?

Here are 5 questions related to this:
1. How do you solve inequalities involving fractions?
2. What happens when you multiply or divide by a negative in inequalities?
3. Can you solve inequalities with absolute values?
4. How do inequalities differ from regular equations?
5. What are the properties of inequalities?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Learn how to solve the inequality -32 - 4u + 5 < -13 with a detailed step-by-step breakdown. This problem covers core algebraic concepts, including combining like terms and the rule for reversing inequality signs when dividing by negative numbers. Suitable for students in Grades 8-10.

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