Find All Complex Solutions x/3-1/4=1/3-x/4

$\frac{x}{3} - \frac{1}{4} = \frac{1}{3} - \frac{x}{4}$

Multiply each term in $\frac{x}{3} - \frac{1}{4} = \frac{1}{3} - \frac{x}{4}$ by $12$ to eliminate the fractions.

Multiply each term in $\frac{x}{3} - \frac{1}{4} = \frac{1}{3} - \frac{x}{4}$ by $12$ .

$\frac{x}{3} \cdot 12 - \frac{1}{4} \cdot 12 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Simplify the left side.

Simplify each term.

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$\frac{x}{3} \cdot (3 (4)) - \frac{1}{4} \cdot 12 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Cancel the common factor.

$\frac{x}{3} \cdot (3 \cdot 4) - \frac{1}{4} \cdot 12 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Rewrite the expression.

$x \cdot 4 - \frac{1}{4} \cdot 12 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Move $4$ to the left of $x$ .

$4 \cdot x - \frac{1}{4} \cdot 12 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$4 x + \frac{- 1}{4} \cdot 12 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Factor $4$ out of $12$ .

$4 x + \frac{- 1}{4} \cdot (4 (3)) = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Cancel the common factor.

$4 x + \frac{- 1}{4} \cdot (4 \cdot 3) = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Rewrite the expression.

$4 x - 1 \cdot 3 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Multiply $- 1$ by $3$ .

$4 x - 3 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$4 x - 3 = \frac{1}{3} \cdot (3 (4)) - \frac{x}{4} \cdot 12$

Cancel the common factor.

$4 x - 3 = \frac{1}{3} \cdot (3 \cdot 4) - \frac{x}{4} \cdot 12$

Rewrite the expression.

$4 x - 3 = 4 - \frac{x}{4} \cdot 12$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{x}{4}$ into the numerator.

$4 x - 3 = 4 + \frac{- x}{4} \cdot 12$

Factor $4$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

$4 x - 3 = 4 - x \cdot 3$

Multiply $3$ by $- 1$ .

$4 x - 3 = 4 - 3 x$

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

Add $3 x$ to both sides of the equation.

$4 x - 3 + 3 x = 4$

Add $4 x$ and $3 x$ .

$7 x - 3 = 4$

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

Add $3$ to both sides of the equation.

$7 x = 4 + 3$

Add $4$ and $3$ .

$7 x = 7$

Divide each term in $7 x = 7$ by $7$ and simplify.

Divide each term in $7 x = 7$ by $7$ .

$\frac{7 x}{7} = \frac{7}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{7}{7}$

Divide $x$ by $1$ .

$x = \frac{7}{7}$

Simplify the right side.

Divide $7$ by $7$ .

$x = 1$

Find All Complex Solutions x/3-1/4=1/3-x/4

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