Solve for x 1/3x+3/5=14/15

$\frac{1}{3} x + \frac{3}{5} = \frac{14}{15}$

Step 1

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} + \frac{3}{5} = \frac{14}{15}$

Step 2

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

Subtract $\frac{3}{5}$ from both sides of the equation.

$\frac{x}{3} = \frac{14}{15} - \frac{3}{5}$

To write $- \frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{3} = \frac{14}{15} - \frac{3}{5} \cdot \frac{3}{3}$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{5}$ by $\frac{3}{3}$ .

$\frac{x}{3} = \frac{14}{15} - \frac{3 \cdot 3}{5 \cdot 3}$

Multiply $5$ by $3$ .

$\frac{x}{3} = \frac{14}{15} - \frac{3 \cdot 3}{15}$

Combine the numerators over the common denominator.

$\frac{x}{3} = \frac{14 - 3 \cdot 3}{15}$

Simplify the numerator.

Multiply $- 3$ by $3$ .

$\frac{x}{3} = \frac{14 - 9}{15}$

Subtract $9$ from $14$ .

$\frac{x}{3} = \frac{5}{15}$

Cancel the common factor of $5$ and $15$ .

Factor $5$ out of $5$ .

$\frac{x}{3} = \frac{5 (1)}{15}$

Cancel the common factors.

Factor $5$ out of $15$ .

$\frac{x}{3} = \frac{5 \cdot 1}{5 \cdot 3}$

Cancel the common factor.

$\frac{x}{3} = \frac{5 \cdot 1}{5 \cdot 3}$

Rewrite the expression.

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

Step 3

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

$x = 1$