Solve for x (2x)/3-x/4=5

$\frac{2 x}{3} - \frac{x}{4} = 5$

Step 1

Simplify $\frac{2 x}{3} - \frac{x}{4}$ .

To write $\frac{2 x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{2 x}{3} \cdot \frac{4}{4} - \frac{x}{4} = 5$

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

$\frac{2 x}{3} \cdot \frac{4}{4} - \frac{x}{4} \cdot \frac{3}{3} = 5$

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

Multiply $\frac{2 x}{3}$ by $\frac{4}{4}$ .

$\frac{2 x \cdot 4}{3 \cdot 4} - \frac{x}{4} \cdot \frac{3}{3} = 5$

Multiply $3$ by $4$ .

$\frac{2 x \cdot 4}{12} - \frac{x}{4} \cdot \frac{3}{3} = 5$

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

$\frac{2 x \cdot 4}{12} - \frac{x \cdot 3}{4 \cdot 3} = 5$

Multiply $4$ by $3$ .

$\frac{2 x \cdot 4}{12} - \frac{x \cdot 3}{12} = 5$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 4 - x \cdot 3}{12} = 5$

Simplify the numerator.

Factor $x$ out of $2 x \cdot 4 - x \cdot 3$ .

Factor $x$ out of $2 x \cdot 4$ .

$\frac{x (2 \cdot 4) - x \cdot 3}{12} = 5$

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

$\frac{x (2 \cdot 4) + x (- 1 \cdot 3)}{12} = 5$

Factor $x$ out of $x (2 \cdot 4) + x (- 1 \cdot 3)$ .

$\frac{x (2 \cdot 4 - 1 \cdot 3)}{12} = 5$

Multiply $2$ by $4$ .

$\frac{x (8 - 1 \cdot 3)}{12} = 5$

Multiply $- 1$ by $3$ .

$\frac{x (8 - 3)}{12} = 5$

Subtract $3$ from $8$ .

$\frac{x \cdot 5}{12} = 5$

Move $5$ to the left of $x$ .

$\frac{5 x}{12} = 5$

Step 2

Multiply both sides of the equation by $\frac{12}{5}$ .

$\frac{12}{5} \cdot \frac{5 x}{12} = \frac{12}{5} \cdot 5$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{12}{5} \cdot \frac{5 x}{12}$ .

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12}{5} \cdot \frac{5 x}{12} = \frac{12}{5} \cdot 5$

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{12}{5} \cdot 5$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{12}{5} \cdot 5$

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{12}{5} \cdot 5$

Rewrite the expression.

$x = \frac{12}{5} \cdot 5$

Simplify the right side.

Cancel the common factor of $5$ .

Cancel the common factor.

$x = \frac{12}{5} \cdot 5$

Rewrite the expression.

$x = 12$

Solve for x (2x)/3-x/4=5

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