Algebra Examples

$x = \frac{1}{3} y z^{2} + 4$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot (y z^{2}) + 4 = x$ .

$\frac{1}{3} \cdot (y z^{2}) + 4 = x$

Step 2

Multiply $\frac{1}{3} (y z^{2})$ .

Tap for more steps...

Step 2.1

Combine $y$ and $\frac{1}{3}$ .

$\frac{y}{3} z^{2} + 4 = x$

Step 2.2

Combine $\frac{y}{3}$ and $z^{2}$ .

$\frac{y z^{2}}{3} + 4 = x$

Step 3

Subtract $4$ from both sides of the equation.

$\frac{y z^{2}}{3} = x - 4$

Step 4

Multiply both sides of the equation by $3$ .

$3 \frac{y z^{2}}{3} = 3 (x - 4)$

Step 5

Simplify both sides of the equation.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.1.1.1

Cancel the common factor.

$3 \frac{y z^{2}}{3} = 3 (x - 4)$

Step 5.1.1.2

Rewrite the expression.

$y z^{2} = 3 (x - 4)$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Simplify $3 (x - 4)$ .

Tap for more steps...

Step 5.2.1.1

Apply the distributive property.

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

Step 5.2.1.2

Multiply $3$ by $- 4$ .

$y z^{2} = 3 x - 12$

Step 6

Divide each term in $y z^{2} = 3 x - 12$ by $z^{2}$ and simplify.

Tap for more steps...

Step 6.1

Divide each term in $y z^{2} = 3 x - 12$ by $z^{2}$ .

$\frac{y z^{2}}{z^{2}} = \frac{3 x}{z^{2}} + \frac{- 12}{z^{2}}$

Step 6.2

Simplify the left side.

Tap for more steps...

Step 6.2.1

Cancel the common factor of $z^{2}$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor.

$\frac{y z^{2}}{z^{2}} = \frac{3 x}{z^{2}} + \frac{- 12}{z^{2}}$

Step 6.2.1.2

Divide $y$ by $1$ .

$y = \frac{3 x}{z^{2}} + \frac{- 12}{z^{2}}$

Step 6.3

Simplify the right side.

Tap for more steps...

Step 6.3.1

Move the negative in front of the fraction.

$y = \frac{3 x}{z^{2}} - \frac{12}{z^{2}}$