Solve -831.45(x/100-298/500)=12.47175(x-298)

$$- 831.45 ( \frac { x } { 100 } - \frac { 298 } { 500 } ) = 12.47175 ( x - 298 )$$

Solve for x

$$x=202.64$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 500, the least common multiple of 100,500.

$$-415725\left(\frac{x}{100}-\frac{298}{500}\right)=6235.875\left(x-298\right)$$

Reduce the fraction \frac{298}{500} to lowest terms by extracting and canceling out 2.

$$-415725\left(\frac{x}{100}-\frac{149}{250}\right)=6235.875\left(x-298\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 100 and 250 is 500. Multiply \frac{x}{100} times \frac{5}{5}. Multiply \frac{149}{250} times \frac{2}{2}.

$$-415725\left(\frac{5x}{500}-\frac{149\times 2}{500}\right)=6235.875\left(x-298\right)$$

Since \frac{5x}{500} and \frac{149\times 2}{500} have the same denominator, subtract them by subtracting their numerators.

$$-415725\times \frac{5x-149\times 2}{500}=6235.875\left(x-298\right)$$

Do the multiplications in 5x-149\times 2.

$$-415725\times \frac{5x-298}{500}=6235.875\left(x-298\right)$$

Express -415725\times \frac{5x-298}{500} as a single fraction.

$$\frac{-415725\left(5x-298\right)}{500}=6235.875\left(x-298\right)$$

Use the distributive property to multiply 6235.875 by x-298.

$$\frac{-415725\left(5x-298\right)}{500}=6235.875x-1858290.75$$

Divide -415725\left(5x-298\right) by 500 to get -\frac{16629}{20}\left(5x-298\right).

$$-\frac{16629}{20}\left(5x-298\right)=6235.875x-1858290.75$$

Use the distributive property to multiply -\frac{16629}{20} by 5x-298.

$$-\frac{16629}{20}\times 5x-\frac{16629}{20}\left(-298\right)=6235.875x-1858290.75$$

Express -\frac{16629}{20}\times 5 as a single fraction.

$$\frac{-16629\times 5}{20}x-\frac{16629}{20}\left(-298\right)=6235.875x-1858290.75$$

Multiply -16629 and 5 to get -83145.

$$\frac{-83145}{20}x-\frac{16629}{20}\left(-298\right)=6235.875x-1858290.75$$

Reduce the fraction \frac{-83145}{20} to lowest terms by extracting and canceling out 5.

$$-\frac{16629}{4}x-\frac{16629}{20}\left(-298\right)=6235.875x-1858290.75$$

Express -\frac{16629}{20}\left(-298\right) as a single fraction.

$$-\frac{16629}{4}x+\frac{-16629\left(-298\right)}{20}=6235.875x-1858290.75$$

Multiply -16629 and -298 to get 4955442.

$$-\frac{16629}{4}x+\frac{4955442}{20}=6235.875x-1858290.75$$

Reduce the fraction \frac{4955442}{20} to lowest terms by extracting and canceling out 2.

$$-\frac{16629}{4}x+\frac{2477721}{10}=6235.875x-1858290.75$$

Subtract 6235.875x from both sides.

$$-\frac{16629}{4}x+\frac{2477721}{10}-6235.875x=-1858290.75$$

Combine -\frac{16629}{4}x and -6235.875x to get -\frac{83145}{8}x.

$$-\frac{83145}{8}x+\frac{2477721}{10}=-1858290.75$$

Subtract \frac{2477721}{10} from both sides.

$$-\frac{83145}{8}x=-1858290.75-\frac{2477721}{10}$$

Convert decimal number -1858290.75 to fraction -\frac{185829075}{100}. Reduce the fraction -\frac{185829075}{100} to lowest terms by extracting and canceling out 25.

$$-\frac{83145}{8}x=-\frac{7433163}{4}-\frac{2477721}{10}$$

Least common multiple of 4 and 10 is 20. Convert -\frac{7433163}{4} and \frac{2477721}{10} to fractions with denominator 20.

$$-\frac{83145}{8}x=-\frac{37165815}{20}-\frac{4955442}{20}$$

Since -\frac{37165815}{20} and \frac{4955442}{20} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{83145}{8}x=\frac{-37165815-4955442}{20}$$

Subtract 4955442 from -37165815 to get -42121257.

$$-\frac{83145}{8}x=-\frac{42121257}{20}$$

Multiply both sides by -\frac{8}{83145}, the reciprocal of -\frac{83145}{8}.

$$x=-\frac{42121257}{20}\left(-\frac{8}{83145}\right)$$

Multiply -\frac{42121257}{20} times -\frac{8}{83145} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-42121257\left(-8\right)}{20\times 83145}$$

Do the multiplications in the fraction \frac{-42121257\left(-8\right)}{20\times 83145}.

$$x=\frac{336970056}{1662900}$$

Reduce the fraction \frac{336970056}{1662900} to lowest terms by extracting and canceling out 66516.

$$x=\frac{5066}{25}$$