Algebra Examples

$w = \frac{x - y}{2} - z$

Step 1

Rewrite the equation as $\frac{x - y}{2} - z = w$ .

$\frac{x - y}{2} - z = w$

Step 2

Simplify $\frac{x - y}{2} - z$ .

Tap for more steps...

Step 2.1

To write $- z$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x - y}{2} - z \cdot \frac{2}{2} = w$

Step 2.2

Combine $- z$ and $\frac{2}{2}$ .

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

Step 2.3

Combine the numerators over the common denominator.

$\frac{x - y - z \cdot 2}{2} = w$

Step 2.4

Multiply $2$ by $- 1$ .

$\frac{x - y - 2 z}{2} = w$

Step 3

Multiply both sides by $2$ .

$\frac{x - y - 2 z}{2} \cdot 2 = w \cdot 2$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor.

$\frac{x - y - 2 z}{2} \cdot 2 = w \cdot 2$

Step 4.1.1.2

Rewrite the expression.

$x - y - 2 z = w \cdot 2$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Move $2$ to the left of $w$ .

$x - y - 2 z = 2 w$

Step 5

Solve for $y$ .

Tap for more steps...

Step 5.1

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

Tap for more steps...

Step 5.1.1

Subtract $x$ from both sides of the equation.

$- y - 2 z = 2 w - x$

Step 5.1.2

Add $2 z$ to both sides of the equation.

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

Step 5.2

Divide each term in $- y = 2 w - x + 2 z$ by $- 1$ and simplify.

Tap for more steps...

Step 5.2.1

Divide each term in $- y = 2 w - x + 2 z$ by $- 1$ .

$\frac{- y}{- 1} = \frac{2 w}{- 1} + \frac{- x}{- 1} + \frac{2 z}{- 1}$

Step 5.2.2

Simplify the left side.

Tap for more steps...

Step 5.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{2 w}{- 1} + \frac{- x}{- 1} + \frac{2 z}{- 1}$

Step 5.2.2.2

Divide $y$ by $1$ .

$y = \frac{2 w}{- 1} + \frac{- x}{- 1} + \frac{2 z}{- 1}$

Step 5.2.3

Simplify the right side.

Tap for more steps...

Step 5.2.3.1

Simplify each term.

Tap for more steps...

Step 5.2.3.1.1

Move the negative one from the denominator of $\frac{2 w}{- 1}$ .

$y = - 1 \cdot (2 w) + \frac{- x}{- 1} + \frac{2 z}{- 1}$

Step 5.2.3.1.2

Rewrite $- 1 \cdot (2 w)$ as $- (2 w)$ .

$y = - (2 w) + \frac{- x}{- 1} + \frac{2 z}{- 1}$

Step 5.2.3.1.3

Multiply $2$ by $- 1$ .

$y = - 2 w + \frac{- x}{- 1} + \frac{2 z}{- 1}$

Step 5.2.3.1.4

Dividing two negative values results in a positive value.

$y = - 2 w + \frac{x}{1} + \frac{2 z}{- 1}$

Step 5.2.3.1.5

Divide $x$ by $1$ .

$y = - 2 w + x + \frac{2 z}{- 1}$

Step 5.2.3.1.6

Move the negative one from the denominator of $\frac{2 z}{- 1}$ .

$y = - 2 w + x - 1 \cdot (2 z)$

Step 5.2.3.1.7

Rewrite $- 1 \cdot (2 z)$ as $- (2 z)$ .

$y = - 2 w + x - (2 z)$

Step 5.2.3.1.8

Multiply $2$ by $- 1$ .

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