Algebra Examples

$x - 2 y = 10$

Subtract $x$ from both sides of the equation.

$- 2 y = - x + 10$

Divide each term by $- 2$ and simplify.

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Divide each term in $- 2 y = - x + 10$ by $- 2$ .

$- \frac{2 y}{- 2} = - \frac{x}{- 2} + \frac{10}{- 2}$

Simplify the left side of the $e q u a t i o n$ by cancelling the common factors.

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Reduce the expression by cancelling the common factors.

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Factor $2$ out of $- 2$ .

$- \frac{2 (y)}{2 (- 1)} = - \frac{x}{- 2} + \frac{10}{- 2}$

Cancel the common factor.

$- \frac{2 y}{2 \cdot - 1} = - \frac{x}{- 2} + \frac{10}{- 2}$

Rewrite the expression.

$- \frac{y}{- 1} = - \frac{x}{- 2} + \frac{10}{- 2}$

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

$- (- 1 \cdot y) = - \frac{x}{- 2} + \frac{10}{- 2}$

Simplify the expression.

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Multiply $- 1$ by $y$ .

$- (- 1 y) = - \frac{x}{- 2} + \frac{10}{- 2}$

Rewrite $- 1 y$ as $- y$ .

$y = - \frac{x}{- 2} + \frac{10}{- 2}$

Simplify each term.

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Move the negative in front of the fraction.

$y = \frac{x}{2} + \frac{10}{- 2}$

Simplify $- - \frac{x}{2}$ .

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Multiply $- 1$ by $- 1$ .

$y = 1 (\frac{x}{2}) + \frac{10}{- 2}$

Multiply $\frac{x}{2}$ by $1$ .

$y = \frac{x}{2} + \frac{10}{- 2}$

Divide $10$ by $- 2$ .

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

To rewrite as a function of $x$ $f (x)$ , 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.

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

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