Basic Math Examples

$y + w - \frac{3}{4} z = 0$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $z$ and $\frac{3}{4}$ .

$y + w - \frac{z \cdot 3}{4} = 0$

Step 1.2

Move $3$ to the left of $z$ .

$y + w - \frac{3 z}{4} = 0$

Step 2

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

Tap for more steps...

Step 2.1

Subtract $y$ from both sides of the equation.

$w - \frac{3 z}{4} = - y$

Step 2.2

Subtract $w$ from both sides of the equation.

$- \frac{3 z}{4} = - y - w$

Step 3

Multiply both sides of the equation by $- \frac{4}{3}$ .

$- \frac{4}{3} (- \frac{3 z}{4}) = - \frac{4}{3} (- y - w)$

Step 4

Simplify both sides of the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Simplify $- \frac{4}{3} (- \frac{3 z}{4})$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.1.1.1.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- 4}{3} (- \frac{3 z}{4}) = - \frac{4}{3} (- y - w)$

Step 4.1.1.1.2

Move the leading negative in $- \frac{3 z}{4}$ into the numerator.

$\frac{- 4}{3} \cdot \frac{- 3 z}{4} = - \frac{4}{3} (- y - w)$

Step 4.1.1.1.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3 z}{4} = - \frac{4}{3} (- y - w)$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3 z}{4} = - \frac{4}{3} (- y - w)$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 z) = - \frac{4}{3} (- y - w)$

Step 4.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.1.1.2.1

Factor $3$ out of $- 3 z$ .

$\frac{- 1}{3} (3 (- z)) = - \frac{4}{3} (- y - w)$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- z)) = - \frac{4}{3} (- y - w)$

Step 4.1.1.2.3

Rewrite the expression.

$- - z = - \frac{4}{3} (- y - w)$

Step 4.1.1.3

Multiply.

Tap for more steps...

Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 z = - \frac{4}{3} (- y - w)$

Step 4.1.1.3.2

Multiply $z$ by $1$ .

$z = - \frac{4}{3} (- y - w)$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $- \frac{4}{3} (- y - w)$ .

Tap for more steps...

Step 4.2.1.1

Apply the distributive property.

$z = - \frac{4}{3} (- y) - \frac{4}{3} (- w)$

Step 4.2.1.2

Multiply $- \frac{4}{3} (- y)$ .

Tap for more steps...

Step 4.2.1.2.1

Multiply $- 1$ by $- 1$ .

$z = 1 (\frac{4}{3}) y - \frac{4}{3} (- w)$

Step 4.2.1.2.2

Multiply $\frac{4}{3}$ by $1$ .

$z = \frac{4}{3} y - \frac{4}{3} (- w)$

Step 4.2.1.2.3

Combine $\frac{4}{3}$ and $y$ .

$z = \frac{4 y}{3} - \frac{4}{3} (- w)$

Step 4.2.1.3

Multiply $- \frac{4}{3} (- w)$ .

Tap for more steps...

Step 4.2.1.3.1

Multiply $- 1$ by $- 1$ .

$z = \frac{4 y}{3} + 1 (\frac{4}{3}) w$

Step 4.2.1.3.2

Multiply $\frac{4}{3}$ by $1$ .

$z = \frac{4 y}{3} + \frac{4}{3} w$

Step 4.2.1.3.3

Combine $\frac{4}{3}$ and $w$ .

$z = \frac{4 y}{3} + \frac{4 w}{3}$

Step 5

Reorder $\frac{4 y}{3}$ and $\frac{4 w}{3}$ .

$z = \frac{4 w}{3} + \frac{4 y}{3}$