Solve for x 2+3/4x=x-3/4

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

Combine $\frac{3}{4}$ and $x$ .

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

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

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

To write $- x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Combine $- x$ and $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $3 x - x \cdot 4$ .

Factor $x$ out of $3 x$ .

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

Factor $x$ out of $- x \cdot 4$ .

$2 + \frac{x \cdot 3 + x (- 1 \cdot 4)}{4} = - \frac{3}{4}$

Factor $x$ out of $x \cdot 3 + x (- 1 \cdot 4)$ .

$2 + \frac{x (3 - 1 \cdot 4)}{4} = - \frac{3}{4}$

Multiply $- 1$ by $4$ .

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

Subtract $4$ from $3$ .

$2 + \frac{x \cdot - 1}{4} = - \frac{3}{4}$

Move $- 1$ to the left of $x$ .

$2 + \frac{- 1 \cdot x}{4} = - \frac{3}{4}$

Move the negative in front of the fraction.

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

Move all terms not containing $x$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

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

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{x}{4} = - \frac{3}{4} - 2 \cdot \frac{4}{4}$

Combine $- 2$ and $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

$- \frac{x}{4} = \frac{- 3 - 2 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 2$ by $4$ .

$- \frac{x}{4} = \frac{- 3 - 8}{4}$

Subtract $8$ from $- 3$ .

$- \frac{x}{4} = \frac{- 11}{4}$

Move the negative in front of the fraction.

$- \frac{x}{4} = - \frac{11}{4}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- x = - 11$

Divide each term in $- x = - 11$ by $- 1$ and simplify.

Divide each term in $- x = - 11$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 11}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 11}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 11}{- 1}$

Simplify the right side.

Divide $- 11$ by $- 1$ .

$x = 11$

Solve for x 2+3/4x=x-3/4

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