Solve for w 5w+9z=2z+3w

$5 w + 9 z = 2 z + 3 w$

Step 1

Move all terms containing $w$ to the left side of the equation.

Subtract $3 w$ from both sides of the equation.

$5 w + 9 z - 3 w = 2 z$

Subtract $3 w$ from $5 w$ .

$2 w + 9 z = 2 z$

Step 2

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

Subtract $9 z$ from both sides of the equation.

$2 w = 2 z - 9 z$

Subtract $9 z$ from $2 z$ .

$2 w = - 7 z$

Step 3

Divide each term in $2 w = - 7 z$ by $2$ and simplify.

Divide each term in $2 w = - 7 z$ by $2$ .

$\frac{2 w}{2} = \frac{- 7 z}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 w}{2} = \frac{- 7 z}{2}$

Divide $w$ by $1$ .

$w = \frac{- 7 z}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$w = - \frac{7 z}{2}$