Finite Math Examples

$2 x + 3 y - z + 2 = 0$

Step 1

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

Tap for more steps...

Step 1.1

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

$3 y - z + 2 = - 2 x$

Step 1.2

Add $z$ to both sides of the equation.

$3 y + 2 = - 2 x + z$

Step 1.3

Subtract $2$ from both sides of the equation.

$3 y = - 2 x + z - 2$

Step 2

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

Tap for more steps...

Step 2.1

Divide each term in $3 y = - 2 x + z - 2$ by $3$ .

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

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $y$ by $1$ .

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

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Simplify each term.

Tap for more steps...

Step 2.3.1.1

Move the negative in front of the fraction.

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

Step 2.3.1.2

Move the negative in front of the fraction.

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

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$