https://file.aiquickdraw.com/mathbot/file/1730057212810qa3mu137.jpg

I see there are several equations that require solving for \( x \) using distribution. Let's go through each equation shown in the image.

### Problem 1
**Equation:**  
\[ 7 + 5(x - 2) = 12 \]

**Solution:**  
1. Distribute the \(5\) across \( (x - 2) \):
   \[
   7 + 5x - 10 = 12
   \]
2. Combine like terms on the left:
   \[
   5x - 3 = 12
   \]
3. Add \(3\) to both sides:
   \[
   5x = 15
   \]
4. Divide by \(5\):
   \[
   x = 3
   \]

### Problem 3
**Equation:**  
\[ 7x + 3(4x - 8) = 109 \]

**Solution:**  
1. Distribute the \(3\) across \( (4x - 8) \):
   \[
   7x + 12x - 24 = 109
   \]
2. Combine like terms on the left:
   \[
   19x - 24 = 109
   \]
3. Add \(24\) to both sides:
   \[
   19x = 133
   \]
4. Divide by \(19\):
   \[
   x = 7
   \]

### Problem 5
**Equation:**  
\[ -4x - 7(-3x - 6) = 195 \]

**Solution:**  
1. Distribute the \(-7\) across \( (-3x - 6) \):
   \[
   -4x + 21x + 42 = 195
   \]
2. Combine like terms on the left:
   \[
   17x + 42 = 195
   \]
3. Subtract \(42\) from both sides:
   \[
   17x = 153
   \]
4. Divide by \(17\):
   \[
   x = 9
   \]

### Problem 7
**Equation:**  
\[ 8(x + 5) + 4 = 60 \]

**Solution:**  
1. Distribute the \(8\) across \( (x + 5) \):
   \[
   8x + 40 + 4 = 60
   \]
2. Combine like terms on the left:
   \[
   8x + 44 = 60
   \]
3. Subtract \(44\) from both sides:
   \[
   8x = 16
   \]
4. Divide by \(8\):
   \[
   x = 2
   \]

Let me know if you need further details on any steps or additional problems solved!

---

### Follow-up Questions:
1. What is the distributive property and how does it work in equations?
2. How do you combine like terms in equations?
3. Why is it important to isolate the variable \(x\) when solving equations?
4. What methods can be used to check solutions after solving?
5. How does one handle negative signs in distribution?

### Tip:
When working with equations, always perform the same operation on both sides to maintain balance!

Solve the following equations using distribution to find x:
1. 7 + 5(x - 2) = 12
3. 7x + 3(4x - 8) = 109
5. -4x - 7(-3x - 6) = 195
7. 8(x + 5) + 4 = 60

Learn how to solve linear equations using the distributive property. Detailed step-by-step solutions to example problems, including combining like terms and isolating the variable.

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