Solve x-2794.8/1906-1800=2797.2-2794.8/200

$$\frac { x - 2794.8 } { 1906 - 1800 } = \frac { 2797.2 - 2794.8 } { 200 }$$

Solve for x

$$x=2796.072$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 200.

$$\frac{100}{53}\left(x-2794.8\right)=2797.2-2794.8$$

Use the distributive property to multiply \frac{100}{53} by x-2794.8.

$$\frac{100}{53}x+\frac{100}{53}\left(-2794.8\right)=2797.2-2794.8$$

Convert decimal number -2794.8 to fraction -\frac{27948}{10}. Reduce the fraction -\frac{27948}{10} to lowest terms by extracting and canceling out 2.

$$\frac{100}{53}x+\frac{100}{53}\left(-\frac{13974}{5}\right)=2797.2-2794.8$$

Multiply \frac{100}{53} times -\frac{13974}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{100}{53}x+\frac{100\left(-13974\right)}{53\times 5}=2797.2-2794.8$$

Do the multiplications in the fraction \frac{100\left(-13974\right)}{53\times 5}.

$$\frac{100}{53}x+\frac{-1397400}{265}=2797.2-2794.8$$

Reduce the fraction \frac{-1397400}{265} to lowest terms by extracting and canceling out 5.

$$\frac{100}{53}x-\frac{279480}{53}=2797.2-2794.8$$

Subtract 2794.8 from 2797.2 to get 2.4.

$$\frac{100}{53}x-\frac{279480}{53}=2.4$$

Add \frac{279480}{53} to both sides.

$$\frac{100}{53}x=2.4+\frac{279480}{53}$$

Convert decimal number 2.4 to fraction \frac{24}{10}. Reduce the fraction \frac{24}{10} to lowest terms by extracting and canceling out 2.

$$\frac{100}{53}x=\frac{12}{5}+\frac{279480}{53}$$

Least common multiple of 5 and 53 is 265. Convert \frac{12}{5} and \frac{279480}{53} to fractions with denominator 265.

$$\frac{100}{53}x=\frac{636}{265}+\frac{1397400}{265}$$

Since \frac{636}{265} and \frac{1397400}{265} have the same denominator, add them by adding their numerators.

$$\frac{100}{53}x=\frac{636+1397400}{265}$$

Add 636 and 1397400 to get 1398036.

$$\frac{100}{53}x=\frac{1398036}{265}$$

Multiply both sides by \frac{53}{100}, the reciprocal of \frac{100}{53}.

$$x=\frac{1398036}{265}\times \frac{53}{100}$$

Multiply \frac{1398036}{265} times \frac{53}{100} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1398036\times 53}{265\times 100}$$

Do the multiplications in the fraction \frac{1398036\times 53}{265\times 100}.

$$x=\frac{74095908}{26500}$$

Reduce the fraction \frac{74095908}{26500} to lowest terms by extracting and canceling out 212.

$$x=\frac{349509}{125}$$