Solve for x x/4+(x-1)/3=1/4

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

Simplify $\frac{x}{4} + \frac{x - 1}{3}$ .

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

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

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

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

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

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

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

Multiply $4$ by $3$ .

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

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

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

Multiply $3$ by $4$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Move $3$ to the left of $x$ .

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

Apply the distributive property.

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

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

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

Multiply $- 1$ by $4$ .

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

Add $3 x$ and $4 x$ .

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

Multiply both sides by $12$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$7 x - 4 = \frac{1}{4} \cdot (4 (3))$

Cancel the common factor.

$7 x - 4 = \frac{1}{4} \cdot (4 \cdot 3)$

Rewrite the expression.

$7 x - 4 = 3$

Solve for $x$ .

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

Add $4$ to both sides of the equation.

$7 x = 3 + 4$

Add $3$ and $4$ .

$7 x = 7$

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 $7$ .

$x = 1$

Solve for x x/4+(x-1)/3=1/4

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