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

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

Rewrite the equation as $\frac{x}{4} + \frac{x}{3} = \frac{2}{3}$ .

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

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

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

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

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

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

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

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

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

Multiply $4$ by $3$ .

$\frac{x \cdot 3}{12} + \frac{x}{3} \cdot \frac{4}{4} = \frac{2}{3}$

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

$\frac{x \cdot 3}{12} + \frac{x \cdot 4}{3 \cdot 4} = \frac{2}{3}$

Multiply $3$ by $4$ .

$\frac{x \cdot 3}{12} + \frac{x \cdot 4}{12} = \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{x \cdot 3 + x \cdot 4}{12} = \frac{2}{3}$

Simplify the numerator.

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

$\frac{3 \cdot x + x \cdot 4}{12} = \frac{2}{3}$

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

$\frac{3 x + 4 \cdot x}{12} = \frac{2}{3}$

Add $3 x$ and $4 x$ .

$\frac{7 x}{12} = \frac{2}{3}$

Multiply both sides of the equation by $\frac{12}{7}$ .

$\frac{12}{7} \cdot \frac{7 x}{12} = \frac{12}{7} \cdot \frac{2}{3}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{12}{7} \cdot \frac{7 x}{12}$ .

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12}{7} \cdot \frac{7 x}{12} = \frac{12}{7} \cdot \frac{2}{3}$

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{12}{7} \cdot \frac{2}{3}$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{12}{7} \cdot \frac{2}{3}$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{12}{7} \cdot \frac{2}{3}$

Rewrite the expression.

$x = \frac{12}{7} \cdot \frac{2}{3}$

Simplify the right side.

Simplify $\frac{12}{7} \cdot \frac{2}{3}$ .

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$x = \frac{3 (4)}{7} \cdot \frac{2}{3}$

Cancel the common factor.

$x = \frac{3 \cdot 4}{7} \cdot \frac{2}{3}$

Rewrite the expression.

$x = \frac{4}{7} \cdot 2$

Combine $\frac{4}{7}$ and $2$ .

$x = \frac{4 \cdot 2}{7}$

Multiply $4$ by $2$ .

$x = \frac{8}{7}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{8}{7}$

Decimal Form:

$x = 1.\overline{142857}$

Mixed Number Form:

$x = 1 \frac{1}{7}$

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

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