Let's solve the equation \( \frac{1}{6}(x - \frac{1}{2}) = -\frac{5}{12} \).

### Step 1: Eliminate the fraction outside the parentheses
Multiply both sides by 6 to eliminate the \(\frac{1}{6}\) on the left side:

\[
x - \frac{1}{2} = 6 \times \left( -\frac{5}{12} \right)
\]

### Step 2: Simplify the right-hand side
On the right-hand side, simplify the multiplication:

\[
x - \frac{1}{2} = -\frac{30}{12}
\]

Reduce \(\frac{30}{12}\):

\[
x - \frac{1}{2} = -\frac{5}{2}
\]

### Step 3: Solve for \(x\)
Add \(\frac{1}{2}\) to both sides:

\[
x = -\frac{5}{2} + \frac{1}{2}
\]

### Step 4: Simplify the right-hand side
Combine the fractions:

\[
x = \frac{-5 + 1}{2} = \frac{-4}{2} = -2
\]

### Final Solution:
\[
x = -2
\]

Would you like further details on any part of this process?

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Here are some related questions:

1. How do you solve similar equations involving fractions?
2. What happens when you multiply or divide both sides of an equation by a fraction?
3. How can you verify your solution to an equation?
4. Can you solve an equation involving variables on both sides?
5. How do you handle equations with fractions in both terms?

**Tip**: Always check your solution by substituting it back into the original equation.

Learn how to solve the linear equation 1/6(x - 1/2) = -5/12 with a detailed step-by-step solution. This problem involves key algebraic concepts such as working with fractions and solving linear equations. Suitable for students in Grades 7-8.

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