Solve 4/5*1/2=2/3*3/x

$$\frac{ 4 }{ 5 } \times \frac{ 1 }{ 2 } = \frac{ 2 }{ 3 } \times \frac{ 3 }{ x }$$

Solve for x

$$x=5$$

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 30x, the least common multiple of 5,2,3,x.

$$\frac{4}{5}\times \frac{1}{2}\times 30x=\frac{2}{3}\times 30\times 3$$

Multiply \frac{4}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 1}{5\times 2}\times 30x=\frac{2}{3}\times 30\times 3$$

Do the multiplications in the fraction \frac{4\times 1}{5\times 2}.

$$\frac{4}{10}\times 30x=\frac{2}{3}\times 30\times 3$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}\times 30x=\frac{2}{3}\times 30\times 3$$

Express \frac{2}{5}\times 30 as a single fraction.

$$\frac{2\times 30}{5}x=\frac{2}{3}\times 30\times 3$$

Multiply 2 and 30 to get 60.

$$\frac{60}{5}x=\frac{2}{3}\times 30\times 3$$

Divide 60 by 5 to get 12.

$$12x=\frac{2}{3}\times 30\times 3$$

Express \frac{2}{3}\times 30 as a single fraction.

$$12x=\frac{2\times 30}{3}\times 3$$

Multiply 2 and 30 to get 60.

$$12x=\frac{60}{3}\times 3$$

Divide 60 by 3 to get 20.

$$12x=20\times 3$$

Multiply 20 and 3 to get 60.

$$12x=60$$

Divide both sides by 12.

$$x=\frac{60}{12}$$

Divide 60 by 12 to get 5.

$$x=5$$