Solve for Q Px-45=Qx+75

$P x - 45 = Q x + 75$

Rewrite the equation as $Q x + 75 = P x - 45$ .

$Q x + 75 = P x - 45$

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

Subtract $75$ from both sides of the equation.

$Q x = P x - 45 - 75$

Subtract $75$ from $- 45$ .

$Q x = P x - 120$

Divide each term in $Q x = P x - 120$ by $x$ and simplify.

Divide each term in $Q x = P x - 120$ by $x$ .

$\frac{Q x}{x} = \frac{P x}{x} + \frac{- 120}{x}$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{Q x}{x} = \frac{P x}{x} + \frac{- 120}{x}$

Divide $Q$ by $1$ .

$Q = \frac{P x}{x} + \frac{- 120}{x}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $x$ .

Cancel the common factor.

$Q = \frac{P x}{x} + \frac{- 120}{x}$

Divide $P$ by $1$ .

$Q = P + \frac{- 120}{x}$

Move the negative in front of the fraction.

$Q = P - \frac{120}{x}$