https://file.aiquickdraw.com/mathbot/file/1724775955839yvt6wnbk.jpg

To solve the problems on the uploaded image, let's go through each of them step by step.

### Problem 1:
\[ 2x + 3 = 9 \]

**Solution:**
1. Subtract 3 from both sides:
   \[
   2x = 6
   \]
2. Divide by 2:
   \[
   x = 3
   \]

### Problem 2:
\[ 3x - 2 = 7 \]

**Solution:**
1. Add 2 to both sides:
   \[
   3x = 9
   \]
2. Divide by 3:
   \[
   x = 3
   \]

### Problem 3:
\[ 4x = 2x + 6 \]

**Solution:**
1. Subtract \(2x\) from both sides:
   \[
   2x = 6
   \]
2. Divide by 2:
   \[
   x = 3
   \]

### Problem 4:
\[ \frac{x - 5}{2} + \frac{3x + 5}{6} = 6 \]

**Solution:**
1. Multiply the entire equation by 6 (to eliminate the denominators):
   \[
   3(x - 5) + (3x + 5) = 36
   \]
2. Distribute and simplify:
   \[
   3x - 15 + 3x + 5 = 36
   \]
   \[
   6x - 10 = 36
   \]
3. Add 10 to both sides:
   \[
   6x = 46
   \]
4. Divide by 6:
   \[
   x = \frac{46}{6} = \frac{23}{3}
   \]

### Problem 5:
\[ 12 \left(\frac{2a - 5}{3} - \frac{a - 3}{4}\right) \]

**Solution:**
1. Simplify inside the parentheses by finding a common denominator:
   \[
   \frac{4(2a - 5)}{12} - \frac{3(a - 3)}{12} = \frac{8a - 20 - 3a + 9}{12} = \frac{5a -

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