Let's simplify the given expression step by step:

The expression is:

\[
\frac{3}{2} \times (2x + 4x + 6)
\]

1. First, combine like terms inside the parentheses:

\[
2x + 4x + 6 = 6x + 6
\]

So, the expression becomes:

\[
\frac{3}{2} \times (6x + 6)
\]

2. Next, distribute \(\frac{3}{2}\) across the terms inside the parentheses:

\[
\frac{3}{2} \times 6x + \frac{3}{2} \times 6
\]

3. Simplify each term:

\[
\frac{3 \times 6x}{2} + \frac{3 \times 6}{2} = \frac{18x}{2} + \frac{18}{2}
\]

4. Divide the terms:

\[
9x + 9
\]

So, the simplified expression is:

\[
9x + 9
\]

Would you like more details or have any questions?

Here are five related questions you might find helpful:
1. How do you distribute fractions over expressions with multiple terms?
2. What are the steps to factor an expression like \(9x + 9\)?
3. How do you simplify expressions involving both fractions and variables?
4. What would happen if the expression inside the parentheses were different, such as \(2x + 5x + 6\)?
5. Can you explain how to solve equations after simplifying expressions like this?

**Tip:** Always combine like terms first before applying distribution to simplify expressions effectively.

Learn how to simplify the expression 3/2(2x + 4x + 6) step-by-step with detailed explanations. This problem covers algebraic concepts such as the distributive property and simplifying expressions involving variables and fractions. Suitable for students in Grades 7-9.

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