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!

Learn how to solve the equation 2 + (3/4)x = x - (3/4) with a detailed step-by-step solution. This problem involves solving linear equations with fractions and is suitable for students in Grades 7-9.

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