To solve the equation $2 + \frac{3}{4}x = x - \frac{3}{4}$, follow these steps:

Step 1: Eliminate the fractions.

Multiply every term by 4 (the denominator of the fractions) to eliminate the fractions:

$4 \times 2 + 4 \times \frac{3}{4}x = 4 \times x - 4 \times \frac{3}{4}$

This simplifies to:

$8 + 3x = 4x - 3$

Step 2: Rearrange the equation.

Move all the terms involving $x$ to one side and the constant terms to the other side:

$8 + 3 = 4x - 3x$

This simplifies to:

$11 = x$

So, the solution is $x = 11$.

Would you like further details or have any questions?

Here are 5 related questions:

1. What happens if you multiply both sides of the equation by a different number?
2. How would the solution change if the equation were $2 - \frac{3}{4}x = x + \frac{3}{4}$?
3. Can you solve for $x$ if the equation includes another variable?
4. How do you graph the equation $2 + \frac{3}{4}x = x - \frac{3}{4}$?
5. What if the equation had more fractions with different denominators?

Tip: Always remember to check your solution by substituting the value of $x$ back into the original equation to verify the result!