Solve for x m(2-x)=5-y

$m (2 - x) = 5 - y$

Step 1

Divide each term in $m (2 - x) = 5 - y$ by $m$ and simplify.

Divide each term in $m (2 - x) = 5 - y$ by $m$ .

$\frac{m (2 - x)}{m} = \frac{5}{m} + \frac{- y}{m}$

Simplify the left side.

Cancel the common factor of $m$ .

Cancel the common factor.

$\frac{m (2 - x)}{m} = \frac{5}{m} + \frac{- y}{m}$

Divide $2 - x$ by $1$ .

$2 - x = \frac{5}{m} + \frac{- y}{m}$

Simplify the right side.

Move the negative in front of the fraction.

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

Step 2

Subtract $2$ from both sides of the equation.

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

Step 3

Divide each term in $- x = \frac{5}{m} - \frac{y}{m} - 2$ by $- 1$ and simplify.

Divide each term in $- x = \frac{5}{m} - \frac{y}{m} - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{\frac{5}{m}}{- 1} + \frac{- \frac{y}{m}}{- 1} + \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{\frac{5}{m}}{- 1} + \frac{- \frac{y}{m}}{- 1} + \frac{- 2}{- 1}$

Divide $x$ by $1$ .

$x = \frac{\frac{5}{m}}{- 1} + \frac{- \frac{y}{m}}{- 1} + \frac{- 2}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{\frac{5}{m}}{- 1}$ .

$x = - 1 \cdot \frac{5}{m} + \frac{- \frac{y}{m}}{- 1} + \frac{- 2}{- 1}$

Rewrite $- 1 \cdot \frac{5}{m}$ as $- \frac{5}{m}$ .

$x = - \frac{5}{m} + \frac{- \frac{y}{m}}{- 1} + \frac{- 2}{- 1}$

Dividing two negative values results in a positive value.

$x = - \frac{5}{m} + \frac{\frac{y}{m}}{1} + \frac{- 2}{- 1}$

Divide $\frac{y}{m}$ by $1$ .

$x = - \frac{5}{m} + \frac{y}{m} + \frac{- 2}{- 1}$

Divide $- 2$ by $- 1$ .

$x = - \frac{5}{m} + \frac{y}{m} + 2$