Solve 890.3x+1559.8left(10/22.4-xright)=480

$$890.3x+1559.8 \left( \frac{ 10 }{ 22.4 } -x \right) = 480$$

Solve for x

$$x=\frac{12115}{37492}\approx 0.323135602$$

Steps for Solving Linear Equation

Expand \frac{10}{22.4} by multiplying both numerator and the denominator by 10.

$$890.3x+1559.8\left(\frac{100}{224}-x\right)=480$$

Reduce the fraction \frac{100}{224} to lowest terms by extracting and canceling out 4.

$$890.3x+1559.8\left(\frac{25}{56}-x\right)=480$$

Use the distributive property to multiply 1559.8 by \frac{25}{56}-x.

$$890.3x+1559.8\times \frac{25}{56}-1559.8x=480$$

Convert decimal number 1559.8 to fraction \frac{15598}{10}. Reduce the fraction \frac{15598}{10} to lowest terms by extracting and canceling out 2.

$$890.3x+\frac{7799}{5}\times \frac{25}{56}-1559.8x=480$$

Multiply \frac{7799}{5} times \frac{25}{56} by multiplying numerator times numerator and denominator times denominator.

$$890.3x+\frac{7799\times 25}{5\times 56}-1559.8x=480$$

Do the multiplications in the fraction \frac{7799\times 25}{5\times 56}.

$$890.3x+\frac{194975}{280}-1559.8x=480$$

Reduce the fraction \frac{194975}{280} to lowest terms by extracting and canceling out 5.

$$890.3x+\frac{38995}{56}-1559.8x=480$$

Combine 890.3x and -1559.8x to get -669.5x.

$$-669.5x+\frac{38995}{56}=480$$

Subtract \frac{38995}{56} from both sides.

$$-669.5x=480-\frac{38995}{56}$$

Convert 480 to fraction \frac{26880}{56}.

$$-669.5x=\frac{26880}{56}-\frac{38995}{56}$$

Since \frac{26880}{56} and \frac{38995}{56} have the same denominator, subtract them by subtracting their numerators.

$$-669.5x=\frac{26880-38995}{56}$$

Subtract 38995 from 26880 to get -12115.

$$-669.5x=-\frac{12115}{56}$$

Divide both sides by -669.5.

$$x=\frac{-\frac{12115}{56}}{-669.5}$$

Express \frac{-\frac{12115}{56}}{-669.5} as a single fraction.

$$x=\frac{-12115}{56\left(-669.5\right)}$$

Multiply 56 and -669.5 to get -37492.

$$x=\frac{-12115}{-37492}$$

Fraction \frac{-12115}{-37492} can be simplified to \frac{12115}{37492} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{12115}{37492}$$