Solve -x=left(27.81left(x-263right)+4.4818left(x-273right)right)left(1/20*85+0.024right)-294

$$-x = \left( 27.81 \left( x-263 \right) +4.4818 \left( x-273 \right) \right) \left( \frac{ 1 }{ 20 \cdot 85 } +0.024 \right) -294$$

Solve for x

$$x = \frac{7138917221}{25414977} = 280\frac{22723661}{25414977} \approx 280.894105118$$

Steps for Solving Linear Equation

Use the distributive property to multiply 27.81 by x-263.

$$-x=\left(27.81x-7314.03+4.4818\left(x-273\right)\right)\left(\frac{1}{20\times 85}+0.024\right)-294$$

Use the distributive property to multiply 4.4818 by x-273.

$$-x=\left(27.81x-7314.03+4.4818x-1223.5314\right)\left(\frac{1}{20\times 85}+0.024\right)-294$$

Combine 27.81x and 4.4818x to get 32.2918x.

$$-x=\left(32.2918x-7314.03-1223.5314\right)\left(\frac{1}{20\times 85}+0.024\right)-294$$

Subtract 1223.5314 from -7314.03 to get -8537.5614.

$$-x=\left(32.2918x-8537.5614\right)\left(\frac{1}{20\times 85}+0.024\right)-294$$

Multiply 20 and 85 to get 1700.

$$-x=\left(32.2918x-8537.5614\right)\left(\frac{1}{1700}+0.024\right)-294$$

Convert decimal number 0.024 to fraction \frac{24}{1000}. Reduce the fraction \frac{24}{1000} to lowest terms by extracting and canceling out 8.

$$-x=\left(32.2918x-8537.5614\right)\left(\frac{1}{1700}+\frac{3}{125}\right)-294$$

Least common multiple of 1700 and 125 is 8500. Convert \frac{1}{1700} and \frac{3}{125} to fractions with denominator 8500.

$$-x=\left(32.2918x-8537.5614\right)\left(\frac{5}{8500}+\frac{204}{8500}\right)-294$$

Since \frac{5}{8500} and \frac{204}{8500} have the same denominator, add them by adding their numerators.

$$-x=\left(32.2918x-8537.5614\right)\times \frac{5+204}{8500}-294$$

Add 5 and 204 to get 209.

$$-x=\left(32.2918x-8537.5614\right)\times \frac{209}{8500}-294$$

Use the distributive property to multiply 32.2918x-8537.5614 by \frac{209}{8500}.

$$-x=32.2918x\times \frac{209}{8500}-8537.5614\times \frac{209}{8500}-294$$

Convert decimal number 32.2918 to fraction \frac{322918}{10000}. Reduce the fraction \frac{322918}{10000} to lowest terms by extracting and canceling out 2.

$$-x=\frac{161459}{5000}x\times \frac{209}{8500}-8537.5614\times \frac{209}{8500}-294$$

Multiply \frac{161459}{5000} times \frac{209}{8500} by multiplying numerator times numerator and denominator times denominator.

$$-x=\frac{161459\times 209}{5000\times 8500}x-8537.5614\times \frac{209}{8500}-294$$

Do the multiplications in the fraction \frac{161459\times 209}{5000\times 8500}.

$$-x=\frac{33744931}{42500000}x-8537.5614\times \frac{209}{8500}-294$$

Convert decimal number -8537.5614 to fraction -\frac{85375614}{10000}. Reduce the fraction -\frac{85375614}{10000} to lowest terms by extracting and canceling out 2.

$$-x=\frac{33744931}{42500000}x-\frac{42687807}{5000}\times \frac{209}{8500}-294$$

Multiply -\frac{42687807}{5000} times \frac{209}{8500} by multiplying numerator times numerator and denominator times denominator.

$$-x=\frac{33744931}{42500000}x+\frac{-42687807\times 209}{5000\times 8500}-294$$

Do the multiplications in the fraction \frac{-42687807\times 209}{5000\times 8500}.

$$-x=\frac{33744931}{42500000}x+\frac{-8921751663}{42500000}-294$$

Fraction \frac{-8921751663}{42500000} can be rewritten as -\frac{8921751663}{42500000} by extracting the negative sign.

$$-x=\frac{33744931}{42500000}x-\frac{8921751663}{42500000}-294$$

Convert 294 to fraction \frac{12495000000}{42500000}.

$$-x=\frac{33744931}{42500000}x-\frac{8921751663}{42500000}-\frac{12495000000}{42500000}$$

Since -\frac{8921751663}{42500000} and \frac{12495000000}{42500000} have the same denominator, subtract them by subtracting their numerators.

$$-x=\frac{33744931}{42500000}x+\frac{-8921751663-12495000000}{42500000}$$

Subtract 12495000000 from -8921751663 to get -21416751663.

$$-x=\frac{33744931}{42500000}x-\frac{21416751663}{42500000}$$

Subtract \frac{33744931}{42500000}x from both sides.

$$-x-\frac{33744931}{42500000}x=-\frac{21416751663}{42500000}$$

Combine -x and -\frac{33744931}{42500000}x to get -\frac{76244931}{42500000}x.

$$-\frac{76244931}{42500000}x=-\frac{21416751663}{42500000}$$

Multiply both sides by -\frac{42500000}{76244931}, the reciprocal of -\frac{76244931}{42500000}.

$$x=-\frac{21416751663}{42500000}\left(-\frac{42500000}{76244931}\right)$$

Multiply -\frac{21416751663}{42500000} times -\frac{42500000}{76244931} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-21416751663\left(-42500000\right)}{42500000\times 76244931}$$

Do the multiplications in the fraction \frac{-21416751663\left(-42500000\right)}{42500000\times 76244931}.

$$x=\frac{910211945677500000}{3240409567500000}$$

Reduce the fraction \frac{910211945677500000}{3240409567500000} to lowest terms by extracting and canceling out 127500000.

$$x=\frac{7138917221}{25414977}$$