Solve for x.

Question

2+3/4x=x–3/4

Answer 1

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

1. First, let's isolate the terms involving \(x\) on one side of the equation. Start by subtracting \(\frac{3}{4}x\) from both sides:

   \[ 2 = x - \frac{3}{4} - \frac{3}{4}x \]

2. Combine the \(x\) terms on the right side:

   \[ 2 = x - \frac{3}{4}x - \frac{3}{4} \]

   This simplifies to:

   \[ 2 = \left(1 - \frac{3}{4}\right)x - \frac{3}{4} \]

   \[ 2 = \frac{1}{4}x - \frac{3}{4} \]

3. Now, add \(\frac{3}{4}\) to both sides to isolate the term with \(x\):

   \[ 2 + \frac{3}{4} = \frac{1}{4}x \]

   Convert \(2\) to a fraction with a denominator of \(4\):

   \[ 2 = \frac{8}{4} \]

   So,

   \[ \frac{8}{4} + \frac{3}{4} = \frac{11}{4} \]

   Now, we have:

   \[ \frac{11}{4} = \frac{1}{4}x \]

4. To solve for \(x\), multiply both sides by \(4\):

   \[ 11 = x \]

Thus, the solution is:

\[ \boxed{11} \]