Solve 1/q=1/33-1/93

$$\frac { 1 } { q } = \frac { 1 } { 33 } - \frac { 1 } { 93 }$$

Solve for q

$$q = \frac{1023}{20} = 51\frac{3}{20} = 51.15$$

Steps for Solving Linear Equation

Variable q cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 1023q, the least common multiple of q,33,93.

$$1023=1023q\times \frac{1}{33}+1023q\left(-\frac{1}{93}\right)$$

Multiply 1023 and \frac{1}{33} to get \frac{1023}{33}.

$$1023=\frac{1023}{33}q+1023q\left(-\frac{1}{93}\right)$$

Divide 1023 by 33 to get 31.

$$1023=31q+1023q\left(-\frac{1}{93}\right)$$

Express 1023\left(-\frac{1}{93}\right) as a single fraction.

$$1023=31q+\frac{1023\left(-1\right)}{93}q$$

Multiply 1023 and -1 to get -1023.

$$1023=31q+\frac{-1023}{93}q$$

Divide -1023 by 93 to get -11.

$$1023=31q-11q$$

Combine 31q and -11q to get 20q.

$$1023=20q$$

Swap sides so that all variable terms are on the left hand side.

$$20q=1023$$

Divide both sides by 20.

$$q=\frac{1023}{20}$$