Algebra Examples

$\frac{5 x - 5 y}{5} = - 6$

Step 1

Cancel the common factor of $5 x - 5 y$ and $5$ .

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Step 1.1

Factor $5$ out of $5 x$ .

$\frac{5 (x) - 5 y}{5} = - 6$

Step 1.2

Factor $5$ out of $- 5 y$ .

$\frac{5 (x) + 5 (- y)}{5} = - 6$

Step 1.3

Factor $5$ out of $5 (x) + 5 (- y)$ .

$\frac{5 (x - y)}{5} = - 6$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $5$ out of $5$ .

$\frac{5 (x - y)}{5 (1)} = - 6$

Step 1.4.2

Cancel the common factor.

$\frac{5 (x - y)}{5 \cdot 1} = - 6$

Step 1.4.3

Rewrite the expression.

$\frac{x - y}{1} = - 6$

Step 1.4.4

Divide $x - y$ by $1$ .

$x - y = - 6$

Step 2

Solve for $y$ .

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Step 2.1

Subtract $x$ from both sides of the equation.

$- y = - 6 - x$

Step 2.2

Divide each term in $- y = - 6 - x$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- y = - 6 - x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 6}{- 1} + \frac{- x}{- 1}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 6}{- 1} + \frac{- x}{- 1}$

Step 2.2.2.2

Divide $y$ by $1$ .

$y = \frac{- 6}{- 1} + \frac{- x}{- 1}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Divide $- 6$ by $- 1$ .

$y = 6 + \frac{- x}{- 1}$

Step 2.2.3.1.2

Dividing two negative values results in a positive value.

$y = 6 + \frac{x}{1}$

Step 2.2.3.1.3

Divide $x$ by $1$ .

$y = 6 + x$

Step 3

To rewrite as a function of $x$ , write the equation so that $y$ is by itself on one side of the equal sign and an expression involving only $x$ is on the other side.

$f (x) = 6 + x$