Let's solve the equation step by step:

The equation is:

\[
\frac{3}{4}x - 12 = \frac{1}{4}x - 6
\]

### Step 1: Eliminate the fractions
To get rid of the fractions, multiply the entire equation by 4, which is the least common denominator:

\[
4 \times \left(\frac{3}{4}x - 12\right) = 4 \times \left(\frac{1}{4}x - 6\right)
\]

Simplifying both sides:

\[
3x - 48 = x - 24
\]

### Step 2: Move the variable terms to one side
Subtract \(x\) from both sides:

\[
3x - x - 48 = -24
\]

This simplifies to:

\[
2x - 48 = -24
\]

### Step 3: Move the constant term to the other side
Add 48 to both sides:

\[
2x = -24 + 48
\]

\[
2x = 24
\]

### Step 4: Solve for \(x\)
Divide both sides by 2:

\[
x = \frac{24}{2} = 12
\]

Thus, the solution is:

\[
x = 12
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you handle equations with fractions and variables on both sides?
2. What is the best way to find the least common denominator in equations?
3. How would you solve an equation with different variable coefficients?
4. What happens when variables cancel out completely on both sides?
5. How can you check if your solution to an equation is correct?

**Tip:** Always simplify both sides of an equation as much as possible before solving for the variable.

Discover how to solve the linear equation 3/4x - 12 = 1/4x - 6. This step-by-step guide covers eliminating fractions, isolating variables, and solving for x. Suitable for students in Grades 7-9 learning algebra and equation-solving techniques.

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