Let's solve the equation $\frac{1}{2}x - 5 = 10 - \frac{3}{4}x$.

Step-by-Step Solution:

1. Eliminate the fractions: Multiply the entire equation by 4, the least common denominator (LCD) of 2 and 4, to get rid of the fractions: $4 \times \left( \frac{1}{2}x - 5 \right) = 4 \times \left( 10 - \frac{3}{4}x \right)$ This simplifies to: $2x - 20 = 40 - 3x$

2. Move all terms with $x$ to one side: Add $3x$ to both sides to bring the terms with $x$ on one side: $2x + 3x - 20 = 40$ Simplifying: $5x - 20 = 40$

3. Isolate $x$: Add 20 to both sides: $5x = 60$

4. Solve for $x$: Divide both sides by 5: $x = 12$

Final Answer:

$x = 12$

Would you like more details or have any questions?

Here are 5 related questions you could explore:

1. How do you solve linear equations with fractions?
2. How do you handle negative numbers when solving equations?
3. Can you explain how to check if a solution to an equation is correct?
4. How would the solution change if the equation had decimals instead of fractions?
5. What happens if both sides of the equation have the same term involving $x$?

Tip: Always clear fractions early in an equation to make solving easier.