Algebra Examples

$- 6 x^{2} - x - 3 y = 4 y$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $4 y$ from both sides of the equation.

$- 6 x^{2} - x - 3 y - 4 y = 0$

Step 1.2

Subtract $4 y$ from $- 3 y$ .

$- 6 x^{2} - x - 7 y = 0$

Step 2

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

Tap for more steps...

Step 2.1

Add $6 x^{2}$ to both sides of the equation.

$- x - 7 y = 6 x^{2}$

Step 2.2

Add $x$ to both sides of the equation.

$- 7 y = 6 x^{2} + x$

Step 3

Divide each term in $- 7 y = 6 x^{2} + x$ by $- 7$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $- 7 y = 6 x^{2} + x$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{6 x^{2}}{- 7} + \frac{x}{- 7}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $- 7$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{6 x^{2}}{- 7} + \frac{x}{- 7}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{6 x^{2}}{- 7} + \frac{x}{- 7}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Simplify each term.

Tap for more steps...

Step 3.3.1.1

Move the negative in front of the fraction.

$y = - \frac{6 x^{2}}{7} + \frac{x}{- 7}$

Step 3.3.1.2

Move the negative in front of the fraction.

$y = - \frac{6 x^{2}}{7} - \frac{x}{7}$

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.

$f (x) = - \frac{6 x^{2}}{7} - \frac{x}{7}$