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.

Learn how to solve the linear equation x/12 - (x - 3)/3 = 1/2 with a detailed step-by-step guide. This problem covers key algebra concepts, including finding a common denominator and using cross-multiplication to solve equations. Suitable for students in Grades 8-10.

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