Algebra Examples

$4 x^{2} - 3 y = - x + 2 y$

Step 1

Move all terms containing $y$ to the left side of the equation.

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Step 1.1

Subtract $2 y$ from both sides of the equation.

$4 x^{2} - 3 y - 2 y = - x$

Step 1.2

Subtract $2 y$ from $- 3 y$ .

$4 x^{2} - 5 y = - x$

Step 2

Subtract $4 x^{2}$ from both sides of the equation.

$- 5 y = - x - 4 x^{2}$

Step 3

Divide each term in $- 5 y = - x - 4 x^{2}$ by $- 5$ and simplify.

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Step 3.1

Divide each term in $- 5 y = - x - 4 x^{2}$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- x}{- 5} + \frac{- 4 x^{2}}{- 5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{- x}{- 5} + \frac{- 4 x^{2}}{- 5}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- x}{- 5} + \frac{- 4 x^{2}}{- 5}$

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

Dividing two negative values results in a positive value.

$y = \frac{x}{5} + \frac{- 4 x^{2}}{- 5}$

Step 3.3.1.2

Dividing two negative values results in a positive value.

$y = \frac{x}{5} + \frac{4 x^{2}}{5}$

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.

$f (x) = \frac{x}{5} + \frac{4 x^{2}}{5}$