https://file.aiquickdraw.com/mathbot/file/1727119401829c1hf451i.jpg

The given expression from the image is:

\[
5(x + 7) + 2(3x - 4)
\]

### Step-by-Step Simplification:

1. **Distribute the terms**:
   - Distribute the 5 across \( (x + 7) \):
     \[
     5(x + 7) = 5x + 35
     \]
   - Distribute the 2 across \( (3x - 4) \):
     \[
     2(3x - 4) = 6x - 8
     \]

2. **Combine like terms**:
   - Now, add the results:
     \[
     (5x + 35) + (6x - 8) = 5x + 6x + 35 - 8
     \]
   - Combine the \(x\)-terms and constants:
     \[
     11x + 27
     \]

### Final Simplified Expression:
\[
11x + 27
\]

Would you like more details, or do you have any questions about the process?

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Here are 5 related questions to consider:
1. What happens when you multiply two binomials, such as \((x + 7)(3x - 4)\)?
2. How can you factor the expression \(11x + 27\)?
3. What are some strategies to solve for \(x\) if you set \(11x + 27 = 0\)?
4. How would the problem change if the expression were \(5(x - 7) + 2(3x + 4)\)?
5. What is the significance of distributing in simplifying algebraic expressions?

**Tip:** When simplifying expressions, always perform distribution first, then combine like terms to keep the process organized.

Learn how to simplify the algebraic expression 5(x + 7) + 2(3x - 4) by distributing terms and combining like terms. Suitable for students in Grades 7-9, this problem highlights key concepts in algebra.

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