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

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

Step 1

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

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

$\frac{x}{3} = - \frac{1}{15} - \frac{3}{5}$

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

$\frac{x}{3} = - \frac{1}{15} - \frac{3}{5} \cdot \frac{3}{3}$

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

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

$\frac{x}{3} = - \frac{1}{15} - \frac{3 \cdot 3}{5 \cdot 3}$

Multiply $5$ by $3$ .

$\frac{x}{3} = - \frac{1}{15} - \frac{3 \cdot 3}{15}$

Combine the numerators over the common denominator.

$\frac{x}{3} = \frac{- 1 - 3 \cdot 3}{15}$

Simplify the numerator.

Multiply $- 3$ by $3$ .

$\frac{x}{3} = \frac{- 1 - 9}{15}$

Subtract $9$ from $- 1$ .

$\frac{x}{3} = \frac{- 10}{15}$

Cancel the common factor of $- 10$ and $15$ .

Factor $5$ out of $- 10$ .

$\frac{x}{3} = \frac{5 (- 2)}{15}$

Cancel the common factors.

Factor $5$ out of $15$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 2

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

$x = - 2$