Solve 4-1/6/x=5/3/18

$$\frac{ 4- \frac{ 1 }{ 6 } }{ x } = \frac{ \frac{ 5 }{ 3 } }{ 18 }$$

Solve for x

$$x = \frac{207}{5} = 41\frac{2}{5} = 41.4$$

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 18x, the least common multiple of x,18.

$$18\left(4-\frac{1}{6}\right)=x\times \frac{5}{3}$$

Convert 4 to fraction \frac{24}{6}.

$$18\left(\frac{24}{6}-\frac{1}{6}\right)=x\times \frac{5}{3}$$

Since \frac{24}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$18\times \frac{24-1}{6}=x\times \frac{5}{3}$$

Subtract 1 from 24 to get 23.

$$18\times \frac{23}{6}=x\times \frac{5}{3}$$

Express 18\times \frac{23}{6} as a single fraction.

$$\frac{18\times 23}{6}=x\times \frac{5}{3}$$

Multiply 18 and 23 to get 414.

$$\frac{414}{6}=x\times \frac{5}{3}$$

Divide 414 by 6 to get 69.

$$69=x\times \frac{5}{3}$$

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

$$x\times \frac{5}{3}=69$$

Multiply both sides by \frac{3}{5}, the reciprocal of \frac{5}{3}.

$$x=69\times \frac{3}{5}$$

Express 69\times \frac{3}{5} as a single fraction.

$$x=\frac{69\times 3}{5}$$

Multiply 69 and 3 to get 207.

$$x=\frac{207}{5}$$