Solve 1/x=1/20+1/40+1/24

$$\frac{ 1 }{ x } = \frac{ 1 }{ 20 } + \frac{ 1 }{ 40 } + \frac{ 1 }{ 24 }$$

Solve for x

$$x = \frac{60}{7} = 8\frac{4}{7} \approx 8.571428571$$

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 120x, the least common multiple of x,20,40,24.

$$120=120x\times \frac{1}{20}+120x\times \frac{1}{40}+120x\times \frac{1}{24}$$

Multiply 120 and \frac{1}{20} to get \frac{120}{20}.

$$120=\frac{120}{20}x+120x\times \frac{1}{40}+120x\times \frac{1}{24}$$

Divide 120 by 20 to get 6.

$$120=6x+120x\times \frac{1}{40}+120x\times \frac{1}{24}$$

Multiply 120 and \frac{1}{40} to get \frac{120}{40}.

$$120=6x+\frac{120}{40}x+120x\times \frac{1}{24}$$

Divide 120 by 40 to get 3.

$$120=6x+3x+120x\times \frac{1}{24}$$

Combine 6x and 3x to get 9x.

$$120=9x+120x\times \frac{1}{24}$$

Multiply 120 and \frac{1}{24} to get \frac{120}{24}.

$$120=9x+\frac{120}{24}x$$

Divide 120 by 24 to get 5.

$$120=9x+5x$$

Combine 9x and 5x to get 14x.

$$120=14x$$

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

$$14x=120$$

Divide both sides by 14.

$$x=\frac{120}{14}$$

Reduce the fraction \frac{120}{14} to lowest terms by extracting and canceling out 2.

$$x=\frac{60}{7}$$