Solve 1/x=1/3+1/6+1/2

$$\frac{ 1 }{ x } = \frac{ 1 }{ 3 } + \frac{ 1 }{ 6 } + \frac{ 1 }{ 2 }$$

Solve for x

$$x=1$$

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 6x, the least common multiple of x,3,6,2.

$$6=6x\times \frac{1}{3}+6x\times \frac{1}{6}+6x\times \frac{1}{2}$$

Multiply 6 and \frac{1}{3} to get \frac{6}{3}.

$$6=\frac{6}{3}x+6x\times \frac{1}{6}+6x\times \frac{1}{2}$$

Divide 6 by 3 to get 2.

$$6=2x+6x\times \frac{1}{6}+6x\times \frac{1}{2}$$

Cancel out 6 and 6.

$$6=2x+x+6x\times \frac{1}{2}$$

Combine 2x and x to get 3x.

$$6=3x+6x\times \frac{1}{2}$$

Multiply 6 and \frac{1}{2} to get \frac{6}{2}.

$$6=3x+\frac{6}{2}x$$

Divide 6 by 2 to get 3.

$$6=3x+3x$$

Combine 3x and 3x to get 6x.

$$6=6x$$

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

$$6x=6$$

Divide both sides by 6.

$$x=\frac{6}{6}$$

Divide 6 by 6 to get 1.

$$x=1$$