Solve for x 6/15=2-x/5

$\frac{6}{15} = 2 - \frac{x}{5}$

Rewrite the equation as $2 - \frac{x}{5} = \frac{6}{15}$ .

$2 - \frac{x}{5} = \frac{6}{15}$

Cancel the common factor of $6$ and $15$ .

Factor $3$ out of $6$ .

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

Cancel the common factors.

Factor $3$ out of $15$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Subtract $2$ from both sides of the equation.

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

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Combine $- 2$ and $\frac{5}{5}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 2$ by $5$ .

$- \frac{x}{5} = \frac{2 - 10}{5}$

Subtract $10$ from $2$ .

$- \frac{x}{5} = \frac{- 8}{5}$

Move the negative in front of the fraction.

$- \frac{x}{5} = - \frac{8}{5}$

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

$- x = - 8$

Divide each term in $- x = - 8$ by $- 1$ and simplify.

Divide each term in $- x = - 8$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 8}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 8}{- 1}$

Simplify the right side.

Divide $- 8$ by $- 1$ .

$x = 8$