Solve 0.1943=x-55.5/201-55.5

$$0.1943 = \frac{ x-55.5 }{ 201-55.5 }$$

Solve for x

$$x=83.77065$$

Steps for Solving Linear Equation

Subtract 55.5 from 201 to get 145.5.

$$0.1943=\frac{x-55.5}{145.5}$$

Divide each term of x-55.5 by 145.5 to get \frac{x}{145.5}+\frac{-55.5}{145.5}.

$$0.1943=\frac{x}{145.5}+\frac{-55.5}{145.5}$$

Expand \frac{-55.5}{145.5} by multiplying both numerator and the denominator by 10.

$$0.1943=\frac{x}{145.5}+\frac{-555}{1455}$$

Reduce the fraction \frac{-555}{1455} to lowest terms by extracting and canceling out 15.

$$0.1943=\frac{x}{145.5}-\frac{37}{97}$$

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

$$\frac{x}{145.5}-\frac{37}{97}=0.1943$$

Add \frac{37}{97} to both sides.

$$\frac{x}{145.5}=0.1943+\frac{37}{97}$$

Convert decimal number 0.1943 to fraction \frac{1943}{10000}.

$$\frac{x}{145.5}=\frac{1943}{10000}+\frac{37}{97}$$

Least common multiple of 10000 and 97 is 970000. Convert \frac{1943}{10000} and \frac{37}{97} to fractions with denominator 970000.

$$\frac{x}{145.5}=\frac{188471}{970000}+\frac{370000}{970000}$$

Since \frac{188471}{970000} and \frac{370000}{970000} have the same denominator, add them by adding their numerators.

$$\frac{x}{145.5}=\frac{188471+370000}{970000}$$

Add 188471 and 370000 to get 558471.

$$\frac{x}{145.5}=\frac{558471}{970000}$$

Multiply both sides by 145.5.

$$x=\frac{558471}{970000}\times 145.5$$

Convert decimal number 145.5 to fraction \frac{1455}{10}. Reduce the fraction \frac{1455}{10} to lowest terms by extracting and canceling out 5.

$$x=\frac{558471}{970000}\times \frac{291}{2}$$

Multiply \frac{558471}{970000} times \frac{291}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{558471\times 291}{970000\times 2}$$

Do the multiplications in the fraction \frac{558471\times 291}{970000\times 2}.

$$x=\frac{162515061}{1940000}$$

Reduce the fraction \frac{162515061}{1940000} to lowest terms by extracting and canceling out 97.

$$x=\frac{1675413}{20000}$$