Let's solve the equation $\frac{3}{4}x - 12 = \frac{1}{2}x - 6$.

Step 1: Eliminate the fractions

To eliminate the fractions, find a common denominator. In this case, the least common denominator between 4 and 2 is 4. Multiply the entire equation by 4:

$4 \left( \frac{3}{4}x - 12 \right) = 4 \left( \frac{1}{2}x - 6 \right)$

This simplifies to:

$3x - 48 = 2x - 24$

Step 2: Move the variable terms to one side

Subtract $2x$ from both sides:

$3x - 2x - 48 = -24$

Simplifying:

$x - 48 = -24$

Step 3: Solve for $x$

Add 48 to both sides:

$x = -24 + 48$

$x = 24$

Final Answer:

The solution is $x = 24$.

Would you like more details on any of the steps?

Here are 5 related questions:

1. How do you solve equations with more complex fractions?
2. What if the equation had fractions with variables in the denominator?
3. How do you handle equations with more than two terms on each side?
4. What methods exist for solving systems of equations?
5. How does solving inequalities differ from solving equalities?

Tip: Always check your solution by substituting it back into the original equation to verify it is correct.