Solve for x w=1/2(x+y-z)

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

Step 1

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

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

Step 2

Multiply both sides of the equation by $2$ .

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

Step 3

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot (x + y - z))$ .

Apply the distributive property.

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

Simplify.

Combine $\frac{1}{2}$ and $x$ .

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

Combine $\frac{1}{2}$ and $y$ .

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

Combine $\frac{1}{2}$ and $z$ .

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

Apply the distributive property.

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

Simplify.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{z}{2}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$x + y - z = 2 w$

Step 4

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

Subtract $y$ from both sides of the equation.

$x - z = 2 w - y$

Add $z$ to both sides of the equation.

$x = 2 w - y + z$