Algebra Examples

$M = \frac{x - y}{9}$

Step 1

Rewrite the equation as $\frac{x - y}{9} = M$ .

$\frac{x - y}{9} = M$

Step 2

Multiply both sides by $9$ .

$\frac{x - y}{9} \cdot 9 = M \cdot 9$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $9$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{x - y}{9} \cdot 9 = M \cdot 9$

Step 3.1.1.2

Rewrite the expression.

$x - y = M \cdot 9$

Step 3.2

Simplify the right side.

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Step 3.2.1

Move $9$ to the left of $M$ .

$x - y = 9 M$

Step 4

Solve for $y$ .

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Step 4.1

Subtract $x$ from both sides of the equation.

$- y = 9 M - x$

Step 4.2

Divide each term in $- y = 9 M - x$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- y = 9 M - x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{9 M}{- 1} + \frac{- x}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{9 M}{- 1} + \frac{- x}{- 1}$

Step 4.2.2.2

Divide $y$ by $1$ .

$y = \frac{9 M}{- 1} + \frac{- x}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Simplify each term.

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Step 4.2.3.1.1

Move the negative one from the denominator of $\frac{9 M}{- 1}$ .

$y = - 1 \cdot (9 M) + \frac{- x}{- 1}$

Step 4.2.3.1.2

Rewrite $- 1 \cdot (9 M)$ as $- (9 M)$ .

$y = - (9 M) + \frac{- x}{- 1}$

Step 4.2.3.1.3

Multiply $9$ by $- 1$ .

$y = - 9 M + \frac{- x}{- 1}$

Step 4.2.3.1.4

Dividing two negative values results in a positive value.

$y = - 9 M + \frac{x}{1}$

Step 4.2.3.1.5

Divide $x$ by $1$ .

$y = - 9 M + x$