We are tasked with solving the equation:

$\frac{x}{12} - \frac{x - 3}{3} = \frac{1}{2}$

Step-by-step solution:

1. Find a common denominator on the left-hand side. The terms have denominators 12 and 3. A common denominator between 12 and 3 is 12.

   Rewrite the second term so that it has a denominator of 12: $\frac{x - 3}{3} = \frac{4(x - 3)}{12} = \frac{4x - 12}{12}$

2. Now the equation becomes: $\frac{x}{12} - \frac{4x - 12}{12} = \frac{1}{2}$

3. Combine the fractions on the left-hand side: $\frac{x - (4x - 12)}{12} = \frac{1}{2}$

   Simplify the numerator: $\frac{x - 4x + 12}{12} = \frac{-3x + 12}{12}$

4. Now the equation is: $\frac{-3x + 12}{12} = \frac{1}{2}$

5. Cross-multiply to eliminate the denominators: $2(-3x + 12) = 12 \times 1$ Simplifying both sides: $-6x + 24 = 12$

6. Solve for $x$: $-6x = 12 - 24$ $-6x = -12$ $x = \frac{-12}{-6} = 2$

Solution:

$x = 2$

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. Solve: $\frac{y}{5} - \frac{y - 4}{2} = \frac{1}{3}$
2. Solve: $\frac{x}{8} - \frac{x - 5}{4} = \frac{2}{3}$
3. Solve: $\frac{2x}{7} - \frac{x - 1}{3} = \frac{1}{2}$
4. Simplify: $\frac{5x - 10}{4} + \frac{3x + 2}{6}$
5. Solve: $\frac{4x + 3}{9} = \frac{x}{2} - \frac{2}{3}$

Tip: Always look for the least common denominator (LCD) to simplify fractions before solving equations.