Solve 12/x=12/8*20/30*1/2

$$\frac { 12 } { x } = \frac { 12 } { 8 } \cdot \frac { 20 } { 30 } \cdot \frac { 1 } { 2 }$$

Solve for x

$$x=24$$

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,8,30,2.

$$120\times 12=15x\times 12\times \frac{20}{30}\times \frac{1}{2}$$

Multiply 120 and 12 to get 1440.

$$1440=15x\times 12\times \frac{20}{30}\times \frac{1}{2}$$

Multiply 15 and 12 to get 180.

$$1440=180x\times \frac{20}{30}\times \frac{1}{2}$$

Reduce the fraction \frac{20}{30} to lowest terms by extracting and canceling out 10.

$$1440=180x\times \frac{2}{3}\times \frac{1}{2}$$

Express 180\times \frac{2}{3} as a single fraction.

$$1440=\frac{180\times 2}{3}x\times \frac{1}{2}$$

Multiply 180 and 2 to get 360.

$$1440=\frac{360}{3}x\times \frac{1}{2}$$

Divide 360 by 3 to get 120.

$$1440=120x\times \frac{1}{2}$$

Multiply 120 and \frac{1}{2} to get \frac{120}{2}.

$$1440=\frac{120}{2}x$$

Divide 120 by 2 to get 60.

$$1440=60x$$

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

$$60x=1440$$

Divide both sides by 60.

$$x=\frac{1440}{60}$$

Divide 1440 by 60 to get 24.

$$x=24$$