Solve for x 5z-2x=3a-2b

$5 z - 2 x = 3 a - 2 b$

Subtract $5 z$ from both sides of the equation.

$- 2 x = 3 a - 2 b - 5 z$

Divide each term in $- 2 x = 3 a - 2 b - 5 z$ by $- 2$ and simplify.

Divide each term in $- 2 x = 3 a - 2 b - 5 z$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{3 a}{- 2} + \frac{- 2 b}{- 2} + \frac{- 5 z}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{3 a}{- 2} + \frac{- 2 b}{- 2} + \frac{- 5 z}{- 2}$

Divide $x$ by $1$ .

$x = \frac{3 a}{- 2} + \frac{- 2 b}{- 2} + \frac{- 5 z}{- 2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{3 a}{2} + \frac{- 2 b}{- 2} + \frac{- 5 z}{- 2}$

Cancel the common factor of $- 2$ .

Cancel the common factor.

$x = - \frac{3 a}{2} + \frac{- 2 b}{- 2} + \frac{- 5 z}{- 2}$

Divide $b$ by $1$ .

$x = - \frac{3 a}{2} + b + \frac{- 5 z}{- 2}$

Dividing two negative values results in a positive value.

$x = - \frac{3 a}{2} + b + \frac{5 z}{2}$