Let's solve the expression:

\[
\frac{3}{2}(4f - 10)
\]

### Step-by-step solution:

1. **Distribute** the \(\frac{3}{2}\) to both terms inside the parentheses:
   \[
   \frac{3}{2} \times 4f = \frac{12f}{2} = 6f
   \]
   \[
   \frac{3}{2} \times (-10) = \frac{-30}{2} = -15
   \]

2. The simplified expression becomes:
   \[
   6f - 15
   \]

So, the expression simplifies to:
\[
6f - 15
\]

Would you like more details or have any questions?

Here are five related questions to expand on this:

1. How do you handle distribution with negative numbers inside parentheses?
2. What is the difference between distributing whole numbers and fractions?
3. How do you solve an equation when variables are present on both sides?
4. How can this expression be used in solving equations?
5. How would this change if you were dealing with division instead of multiplication?

**Tip**: Always simplify fractions first when distributing to make calculations easier.

Explore the step-by-step solution of the algebraic expression 3/2(4f - 10). This problem demonstrates the application of the distributive property to simplify expressions, making it suitable for students in Grades 6-8. Learn how to distribute fractions and simplify algebraic terms with ease.

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