Solve 1/x=-1/12--1/20

$$\frac{ 1 }{ x } = - \frac{ 1 }{ 12 } -- \frac{ 1 }{ 20 }$$

Solve for x

$$x=-30$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 60x, the least common multiple of x,12,20.

$$60=60x\left(-\frac{1}{12}\right)-60x\left(-\frac{1}{20}\right)$$

Express 60\left(-\frac{1}{12}\right) as a single fraction.

$$60=\frac{60\left(-1\right)}{12}x-60x\left(-\frac{1}{20}\right)$$

Multiply 60 and -1 to get -60.

$$60=\frac{-60}{12}x-60x\left(-\frac{1}{20}\right)$$

Divide -60 by 12 to get -5.

$$60=-5x-60x\left(-\frac{1}{20}\right)$$

Express 60\left(-\frac{1}{20}\right) as a single fraction.

$$60=-5x-\frac{60\left(-1\right)}{20}x$$

Multiply 60 and -1 to get -60.

$$60=-5x-\frac{-60}{20}x$$

Divide -60 by 20 to get -3.

$$60=-5x-\left(-3x\right)$$

The opposite of -3x is 3x.

$$60=-5x+3x$$

Combine -5x and 3x to get -2x.

$$60=-2x$$

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

$$-2x=60$$

Divide both sides by -2.

$$x=\frac{60}{-2}$$

Divide 60 by -2 to get -30.

$$x=-30$$