Solve 1/x+20=1/15+1/10

$$\frac { 1 } { x + 20 } = \frac { 1 } { 15 } + \frac { 1 } { 10 }$$

Solve for x

$$x=-14$$

Steps for Solving Linear Equation

Variable x cannot be equal to -20 since division by zero is not defined. Multiply both sides of the equation by 30\left(x+20\right), the least common multiple of x+20,15,10.

$$30=30\left(x+20\right)\times \frac{1}{15}+30\left(x+20\right)\times \frac{1}{10}$$

Multiply 30 and \frac{1}{15} to get 2.

$$30=2\left(x+20\right)+30\left(x+20\right)\times \frac{1}{10}$$

Use the distributive property to multiply 2 by x+20.

$$30=2x+40+30\left(x+20\right)\times \frac{1}{10}$$

Multiply 30 and \frac{1}{10} to get 3.

$$30=2x+40+3\left(x+20\right)$$

Use the distributive property to multiply 3 by x+20.

$$30=2x+40+3x+60$$

Combine 2x and 3x to get 5x.

$$30=5x+40+60$$

Add 40 and 60 to get 100.

$$30=5x+100$$

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

$$5x+100=30$$

Subtract 100 from both sides.

$$5x=30-100$$

Subtract 100 from 30 to get -70.

$$5x=-70$$

Divide both sides by 5.

$$x=\frac{-70}{5}$$

Divide -70 by 5 to get -14.

$$x=-14$$