Solve x-5/100x=(73-x)-7/100(73-x)+17.64

$$x- \frac{ 5 }{ 100 } x=(73-x)- \frac{ 7 }{ 100 } (73-x)+17.64$$

Solve for x

$$x = \frac{8553}{188} = 45\frac{93}{188} \approx 45.494680851$$

Steps for Solving Linear Equation

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$x-\frac{1}{20}x=73-x-\frac{7}{100}\left(73-x\right)+17.64$$

Combine x and -\frac{1}{20}x to get \frac{19}{20}x.

$$\frac{19}{20}x=73-x-\frac{7}{100}\left(73-x\right)+17.64$$

Use the distributive property to multiply -\frac{7}{100} by 73-x.

$$\frac{19}{20}x=73-x-\frac{7}{100}\times 73-\frac{7}{100}\left(-1\right)x+17.64$$

Express -\frac{7}{100}\times 73 as a single fraction.

$$\frac{19}{20}x=73-x+\frac{-7\times 73}{100}-\frac{7}{100}\left(-1\right)x+17.64$$

Multiply -7 and 73 to get -511.

$$\frac{19}{20}x=73-x+\frac{-511}{100}-\frac{7}{100}\left(-1\right)x+17.64$$

Fraction \frac{-511}{100} can be rewritten as -\frac{511}{100} by extracting the negative sign.

$$\frac{19}{20}x=73-x-\frac{511}{100}-\frac{7}{100}\left(-1\right)x+17.64$$

Multiply -\frac{7}{100} and -1 to get \frac{7}{100}.

$$\frac{19}{20}x=73-x-\frac{511}{100}+\frac{7}{100}x+17.64$$

Convert 73 to fraction \frac{7300}{100}.

$$\frac{19}{20}x=\frac{7300}{100}-x-\frac{511}{100}+\frac{7}{100}x+17.64$$

Since \frac{7300}{100} and \frac{511}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19}{20}x=\frac{7300-511}{100}-x+\frac{7}{100}x+17.64$$

Subtract 511 from 7300 to get 6789.

$$\frac{19}{20}x=\frac{6789}{100}-x+\frac{7}{100}x+17.64$$

Combine -x and \frac{7}{100}x to get -\frac{93}{100}x.

$$\frac{19}{20}x=\frac{6789}{100}-\frac{93}{100}x+17.64$$

Convert decimal number 17.64 to fraction \frac{1764}{100}. Reduce the fraction \frac{1764}{100} to lowest terms by extracting and canceling out 4.

$$\frac{19}{20}x=\frac{6789}{100}-\frac{93}{100}x+\frac{441}{25}$$

Least common multiple of 100 and 25 is 100. Convert \frac{6789}{100} and \frac{441}{25} to fractions with denominator 100.

$$\frac{19}{20}x=\frac{6789}{100}-\frac{93}{100}x+\frac{1764}{100}$$

Since \frac{6789}{100} and \frac{1764}{100} have the same denominator, add them by adding their numerators.

$$\frac{19}{20}x=\frac{6789+1764}{100}-\frac{93}{100}x$$

Add 6789 and 1764 to get 8553.

$$\frac{19}{20}x=\frac{8553}{100}-\frac{93}{100}x$$

Add \frac{93}{100}x to both sides.

$$\frac{19}{20}x+\frac{93}{100}x=\frac{8553}{100}$$

Combine \frac{19}{20}x and \frac{93}{100}x to get \frac{47}{25}x.

$$\frac{47}{25}x=\frac{8553}{100}$$

Multiply both sides by \frac{25}{47}, the reciprocal of \frac{47}{25}.

$$x=\frac{8553}{100}\times \frac{25}{47}$$

Multiply \frac{8553}{100} times \frac{25}{47} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{8553\times 25}{100\times 47}$$

Do the multiplications in the fraction \frac{8553\times 25}{100\times 47}.

$$x=\frac{213825}{4700}$$

Reduce the fraction \frac{213825}{4700} to lowest terms by extracting and canceling out 25.

$$x=\frac{8553}{188}$$