Algebra Examples

$x^{2} + x = - x - 3 y$

Step 1

Rewrite the equation as $- x - 3 y = x^{2} + x$ .

$- x - 3 y = x^{2} + x$

Step 2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.1

Add $x$ to both sides of the equation.

$- 3 y = x^{2} + x + x$

Step 2.2

Add $x$ and $x$ .

$- 3 y = x^{2} + 2 x$

Step 3

Divide each term in $- 3 y = x^{2} + 2 x$ by $- 3$ and simplify.

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Step 3.1

Divide each term in $- 3 y = x^{2} + 2 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{x^{2}}{- 3} + \frac{2 x}{- 3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{x^{2}}{- 3} + \frac{2 x}{- 3}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{x^{2}}{- 3} + \frac{2 x}{- 3}$

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 in front of the fraction.

$y = - \frac{x^{2}}{3} + \frac{2 x}{- 3}$

Step 3.3.1.2

Move the negative in front of the fraction.

$y = - \frac{x^{2}}{3} - \frac{2 x}{3}$

Step 4

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.

$f (x) = - \frac{x^{2}}{3} - \frac{2 x}{3}$