Pre-Algebra Examples

$m (5 - x) = 7 - y$

Step 1

Divide each term in $m (5 - x) = 7 - y$ by $m$ and simplify.

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Step 1.1

Divide each term in $m (5 - x) = 7 - y$ by $m$ .

$\frac{m (5 - x)}{m} = \frac{7}{m} + \frac{- y}{m}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $m$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{m (5 - x)}{m} = \frac{7}{m} + \frac{- y}{m}$

Step 1.2.1.2

Divide $5 - x$ by $1$ .

$5 - x = \frac{7}{m} + \frac{- y}{m}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Move the negative in front of the fraction.

$5 - x = \frac{7}{m} - \frac{y}{m}$

Step 2

Subtract $5$ from both sides of the equation.

$- x = \frac{7}{m} - \frac{y}{m} - 5$

Step 3

Divide each term in $- x = \frac{7}{m} - \frac{y}{m} - 5$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- x = \frac{7}{m} - \frac{y}{m} - 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{\frac{7}{m}}{- 1} + \frac{- \frac{y}{m}}{- 1} + \frac{- 5}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{\frac{7}{m}}{- 1} + \frac{- \frac{y}{m}}{- 1} + \frac{- 5}{- 1}$

Step 3.2.2

Divide $x$ by $1$ .

$x = \frac{\frac{7}{m}}{- 1} + \frac{- \frac{y}{m}}{- 1} + \frac{- 5}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Move the negative one from the denominator of $\frac{\frac{7}{m}}{- 1}$ .

$x = - 1 \cdot \frac{7}{m} + \frac{- \frac{y}{m}}{- 1} + \frac{- 5}{- 1}$

Step 3.3.1.2

Rewrite $- 1 \cdot \frac{7}{m}$ as $- \frac{7}{m}$ .

$x = - \frac{7}{m} + \frac{- \frac{y}{m}}{- 1} + \frac{- 5}{- 1}$

Step 3.3.1.3

Dividing two negative values results in a positive value.

$x = - \frac{7}{m} + \frac{\frac{y}{m}}{1} + \frac{- 5}{- 1}$

Step 3.3.1.4

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

$x = - \frac{7}{m} + \frac{y}{m} + \frac{- 5}{- 1}$

Step 3.3.1.5

Divide $- 5$ by $- 1$ .

$x = - \frac{7}{m} + \frac{y}{m} + 5$