Solve (50-5.7x)1/13.1=(5.7x-22)div17.5+x

$$(50-5.7x) \frac{ 1 }{ 13.1 } =(5.7x-22) \div 17.5+x$$

Solve for x

$$x = \frac{116320}{40367} = 2\frac{35586}{40367} \approx 2.881561672$$

Steps for Solving Linear Equation

Expand \frac{1}{13.1} by multiplying both numerator and the denominator by 10.

$$\left(50-5.7x\right)\times \frac{10}{131}=\frac{5.7x-22}{17.5}+x$$

Use the distributive property to multiply 50-5.7x by \frac{10}{131}.

$$50\times \frac{10}{131}-5.7x\times \frac{10}{131}=\frac{5.7x-22}{17.5}+x$$

Express 50\times \frac{10}{131} as a single fraction.

$$\frac{50\times 10}{131}-5.7x\times \frac{10}{131}=\frac{5.7x-22}{17.5}+x$$

Multiply 50 and 10 to get 500.

$$\frac{500}{131}-5.7x\times \frac{10}{131}=\frac{5.7x-22}{17.5}+x$$

Convert decimal number -5.7 to fraction -\frac{57}{10}.

$$\frac{500}{131}-\frac{57}{10}x\times \frac{10}{131}=\frac{5.7x-22}{17.5}+x$$

Multiply -\frac{57}{10} times \frac{10}{131} by multiplying numerator times numerator and denominator times denominator.

$$\frac{500}{131}+\frac{-57\times 10}{10\times 131}x=\frac{5.7x-22}{17.5}+x$$

Cancel out 10 in both numerator and denominator.

$$\frac{500}{131}+\frac{-57}{131}x=\frac{5.7x-22}{17.5}+x$$

Fraction \frac{-57}{131} can be rewritten as -\frac{57}{131} by extracting the negative sign.

$$\frac{500}{131}-\frac{57}{131}x=\frac{5.7x-22}{17.5}+x$$

Divide each term of 5.7x-22 by 17.5 to get \frac{5.7x}{17.5}+\frac{-22}{17.5}.

$$\frac{500}{131}-\frac{57}{131}x=\frac{5.7x}{17.5}+\frac{-22}{17.5}+x$$

Divide 5.7x by 17.5 to get \frac{57}{175}x.

$$\frac{500}{131}-\frac{57}{131}x=\frac{57}{175}x+\frac{-22}{17.5}+x$$

Expand \frac{-22}{17.5} by multiplying both numerator and the denominator by 10.

$$\frac{500}{131}-\frac{57}{131}x=\frac{57}{175}x+\frac{-220}{175}+x$$

Reduce the fraction \frac{-220}{175} to lowest terms by extracting and canceling out 5.

$$\frac{500}{131}-\frac{57}{131}x=\frac{57}{175}x-\frac{44}{35}+x$$

Combine \frac{57}{175}x and x to get \frac{232}{175}x.

$$\frac{500}{131}-\frac{57}{131}x=\frac{232}{175}x-\frac{44}{35}$$

Subtract \frac{232}{175}x from both sides.

$$\frac{500}{131}-\frac{57}{131}x-\frac{232}{175}x=-\frac{44}{35}$$

Combine -\frac{57}{131}x and -\frac{232}{175}x to get -\frac{40367}{22925}x.

$$\frac{500}{131}-\frac{40367}{22925}x=-\frac{44}{35}$$

Subtract \frac{500}{131} from both sides.

$$-\frac{40367}{22925}x=-\frac{44}{35}-\frac{500}{131}$$

Least common multiple of 35 and 131 is 4585. Convert -\frac{44}{35} and \frac{500}{131} to fractions with denominator 4585.

$$-\frac{40367}{22925}x=-\frac{5764}{4585}-\frac{17500}{4585}$$

Since -\frac{5764}{4585} and \frac{17500}{4585} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{40367}{22925}x=\frac{-5764-17500}{4585}$$

Subtract 17500 from -5764 to get -23264.

$$-\frac{40367}{22925}x=-\frac{23264}{4585}$$

Multiply both sides by -\frac{22925}{40367}, the reciprocal of -\frac{40367}{22925}.

$$x=-\frac{23264}{4585}\left(-\frac{22925}{40367}\right)$$

Multiply -\frac{23264}{4585} times -\frac{22925}{40367} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-23264\left(-22925\right)}{4585\times 40367}$$

Do the multiplications in the fraction \frac{-23264\left(-22925\right)}{4585\times 40367}.

$$x=\frac{533327200}{185082695}$$

Reduce the fraction \frac{533327200}{185082695} to lowest terms by extracting and canceling out 4585.

$$x=\frac{116320}{40367}$$