Solve 6+20/100x/100+frac{20{100}}=16/100

$$\frac { 6 + \frac { 20 } { 100 } x } { 100 + \frac { 20 } { 100 } } = \frac { 16 } { 100 }$$

Solve for x

$$x = \frac{1254}{25} = 50\frac{4}{25} = 50.16$$

Steps for Solving Linear Equation

Reduce the fraction \frac{20}{100} to lowest terms by extracting and canceling out 20.

$$\frac{6+\frac{1}{5}x}{100+\frac{20}{100}}=\frac{16}{100}$$

Reduce the fraction \frac{20}{100} to lowest terms by extracting and canceling out 20.

$$\frac{6+\frac{1}{5}x}{100+\frac{1}{5}}=\frac{16}{100}$$

Convert 100 to fraction \frac{500}{5}.

$$\frac{6+\frac{1}{5}x}{\frac{500}{5}+\frac{1}{5}}=\frac{16}{100}$$

Since \frac{500}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\frac{6+\frac{1}{5}x}{\frac{500+1}{5}}=\frac{16}{100}$$

Add 500 and 1 to get 501.

$$\frac{6+\frac{1}{5}x}{\frac{501}{5}}=\frac{16}{100}$$

Reduce the fraction \frac{16}{100} to lowest terms by extracting and canceling out 4.

$$\frac{6+\frac{1}{5}x}{\frac{501}{5}}=\frac{4}{25}$$

Divide each term of 6+\frac{1}{5}x by \frac{501}{5} to get \frac{6}{\frac{501}{5}}+\frac{\frac{1}{5}x}{\frac{501}{5}}.

$$\frac{6}{\frac{501}{5}}+\frac{\frac{1}{5}x}{\frac{501}{5}}=\frac{4}{25}$$

Divide 6 by \frac{501}{5} by multiplying 6 by the reciprocal of \frac{501}{5}.

$$6\times \frac{5}{501}+\frac{\frac{1}{5}x}{\frac{501}{5}}=\frac{4}{25}$$

Express 6\times \frac{5}{501} as a single fraction.

$$\frac{6\times 5}{501}+\frac{\frac{1}{5}x}{\frac{501}{5}}=\frac{4}{25}$$

Multiply 6 and 5 to get 30.

$$\frac{30}{501}+\frac{\frac{1}{5}x}{\frac{501}{5}}=\frac{4}{25}$$

Reduce the fraction \frac{30}{501} to lowest terms by extracting and canceling out 3.

$$\frac{10}{167}+\frac{\frac{1}{5}x}{\frac{501}{5}}=\frac{4}{25}$$

Divide \frac{1}{5}x by \frac{501}{5} to get \frac{1}{501}x.

$$\frac{10}{167}+\frac{1}{501}x=\frac{4}{25}$$

Subtract \frac{10}{167} from both sides.

$$\frac{1}{501}x=\frac{4}{25}-\frac{10}{167}$$

Least common multiple of 25 and 167 is 4175. Convert \frac{4}{25} and \frac{10}{167} to fractions with denominator 4175.

$$\frac{1}{501}x=\frac{668}{4175}-\frac{250}{4175}$$

Since \frac{668}{4175} and \frac{250}{4175} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{501}x=\frac{668-250}{4175}$$

Subtract 250 from 668 to get 418.

$$\frac{1}{501}x=\frac{418}{4175}$$

Multiply both sides by 501, the reciprocal of \frac{1}{501}.

$$x=\frac{418}{4175}\times 501$$

Express \frac{418}{4175}\times 501 as a single fraction.

$$x=\frac{418\times 501}{4175}$$

Multiply 418 and 501 to get 209418.

$$x=\frac{209418}{4175}$$

Reduce the fraction \frac{209418}{4175} to lowest terms by extracting and canceling out 167.

$$x=\frac{1254}{25}$$