Let's simplify the expression:

Given:

\[
3(-3u - 4) + \frac{5}{2}u
\]

### Step 1: Distribute the 3 to the terms inside the parentheses.

\[
3(-3u) + 3(-4) = -9u - 12
\]

Now the expression becomes:

\[
-9u - 12 + \frac{5}{2}u
\]

### Step 2: Combine like terms.
We have two terms with \(u\): \(-9u\) and \(\frac{5}{2}u\).

To combine these, we need a common denominator. The common denominator between \(-9\) and \(\frac{5}{2}\) is 2.

\[
-9u = \frac{-18}{2}u
\]

Now, combine:

\[
\frac{-18}{2}u + \frac{5}{2}u = \frac{-18 + 5}{2}u = \frac{-13}{2}u
\]

### Step 3: Final simplified expression.

Now we rewrite the entire expression:

\[
\frac{-13}{2}u - 12
\]

This is the simplified form of the given expression.

Would you like more details or have any questions? Here are some related questions:

1. How do you find a common denominator when combining fractions?
2. How do you distribute constants across parentheses?
3. What are the properties of combining like terms in algebra?
4. How do you handle mixed fractions in algebraic expressions?
5. How can you solve for \(u\) if the equation was equal to a value?

**Tip**: Always combine like terms with care, especially when dealing with fractions.

Learn how to simplify the algebraic expression 3(-3u - 4) + 5/2u step-by-step. This problem involves the distributive property, combining like terms, and handling fractional coefficients. Perfect for students in Grades 8-10.

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