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 -