Solve for y w=1/7(x+y-z)

$w = \frac{1}{7} (x + y - z)$

Step 1

Rewrite the equation as $\frac{1}{7} \cdot (x + y - z) = w$ .

$\frac{1}{7} \cdot (x + y - z) = w$

Step 2

Multiply both sides of the equation by $7$ .

$7 (\frac{1}{7} \cdot (x + y - z)) = 7 w$

Step 3

Simplify the left side.

Simplify $7 (\frac{1}{7} \cdot (x + y - z))$ .

Apply the distributive property.

$7 (\frac{1}{7} x + \frac{1}{7} y + \frac{1}{7} (- z)) = 7 w$

Simplify.

Combine $\frac{1}{7}$ and $x$ .

$7 (\frac{x}{7} + \frac{1}{7} y + \frac{1}{7} (- z)) = 7 w$

Combine $\frac{1}{7}$ and $y$ .

$7 (\frac{x}{7} + \frac{y}{7} + \frac{1}{7} (- z)) = 7 w$

Combine $\frac{1}{7}$ and $z$ .

$7 (\frac{x}{7} + \frac{y}{7} - \frac{z}{7}) = 7 w$

Apply the distributive property.

$7 \frac{x}{7} + 7 \frac{y}{7} + 7 (- \frac{z}{7}) = 7 w$

Simplify.

Cancel the common factor of $7$ .

Cancel the common factor.

$7 \frac{x}{7} + 7 \frac{y}{7} + 7 (- \frac{z}{7}) = 7 w$

Rewrite the expression.

$x + 7 \frac{y}{7} + 7 (- \frac{z}{7}) = 7 w$

Cancel the common factor of $7$ .

Cancel the common factor.

$x + 7 \frac{y}{7} + 7 (- \frac{z}{7}) = 7 w$

Rewrite the expression.

$x + y + 7 (- \frac{z}{7}) = 7 w$

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{z}{7}$ into the numerator.

$x + y + 7 \frac{- z}{7} = 7 w$

Cancel the common factor.

$x + y + 7 \frac{- z}{7} = 7 w$

Rewrite the expression.

$x + y - z = 7 w$

Step 4

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

Subtract $x$ from both sides of the equation.

$y - z = 7 w - x$

Add $z$ to both sides of the equation.

$y = 7 w - x + z$