Let's simplify the expression \(3(2x + 4) + 7\).

1. **Distribute** \(3\) to both terms inside the parentheses:
   \[
   3 \cdot 2x + 3 \cdot 4 = 6x + 12
   \]

2. **Rewrite the expression** after distribution:
   \[
   6x + 12 + 7
   \]

3. **Combine like terms** \(12\) and \(7\):
   \[
   6x + 19
   \]

So, the simplified expression is:
\[
6x + 19
\]

Would you like more details or have any questions?

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1. How would the solution change if the expression were \(3(2x - 4) + 7\)?
2. What is the result if we add another term, say \(5x\), to \(6x + 19\)?
3. How do we handle expressions like \(3(2x + 4) + 7x\)?
4. What are similar simplification techniques for expressions with three terms, like \(3(2x + 4) + 7 + 2x\)?
5. Can you factor the expression \(6x + 19\) further?

**Tip:** When simplifying, distribute first, then combine like terms for a cleaner result.

Learn how to simplify the algebraic expression 3(2x + 4) + 7 with step-by-step instructions. This problem uses the distributive property and combines like terms, making it ideal for students in Grades 6-8.

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