Solve for x x/3-1/4=1/3-x/4

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

Step 1

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

Add $\frac{x}{4}$ to both sides of the equation.

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

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{3}$ by $\frac{4}{4}$ .

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

Multiply $3$ by $4$ .

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

Multiply $\frac{x}{4}$ by $\frac{3}{3}$ .

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

Multiply $4$ by $3$ .

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

Combine the numerators over the common denominator.

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

Reorder $x$ and $3$ .

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

Add $4 \cdot x$ and $3 \cdot x$ .

$\frac{7 x}{12} - \frac{1}{4} = \frac{1}{3}$

Step 2

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

Add $\frac{1}{4}$ to both sides of the equation.

$\frac{7 x}{12} = \frac{1}{3} + \frac{1}{4}$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7 x}{12} = \frac{1}{3} \cdot \frac{4}{4} + \frac{1}{4}$

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7 x}{12} = \frac{1}{3} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{3}{3}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$\frac{7 x}{12} = \frac{4}{3 \cdot 4} + \frac{1}{4} \cdot \frac{3}{3}$

Multiply $3$ by $4$ .

$\frac{7 x}{12} = \frac{4}{12} + \frac{1}{4} \cdot \frac{3}{3}$

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{7 x}{12} = \frac{4}{12} + \frac{3}{4 \cdot 3}$

Multiply $4$ by $3$ .

$\frac{7 x}{12} = \frac{4}{12} + \frac{3}{12}$

Combine the numerators over the common denominator.

$\frac{7 x}{12} = \frac{4 + 3}{12}$

Add $4$ and $3$ .

$\frac{7 x}{12} = \frac{7}{12}$

Step 3

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

$7 x = 7$

Step 4

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 $7$ .

$x = 1$

Solve for x x/3-1/4=1/3-x/4

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