Solve -x=left(27.81*85left(x-263right)+4.9712*85left(x-273right)right)left(1/20*85+0.024right)-294

$$-x = \left( 27.81 \times 85 \left( x-263 \right) +4.9712 \times 85 \left( x-273 \right) \right) \left( \frac{ 1 }{ 20 \cdot 85 } +0.024 \right) -294$$

Solve for x

$$x = \frac{4604185071}{17378177} = 264\frac{16346343}{17378177} \approx 264.940624727$$

Steps for Solving Linear Equation

Multiply 27.81 and 85 to get 2363.85.

$$-x=\left(2363.85\left(x-263\right)+4.9712\times 85\left(x-273\right)\right)\left(\frac{1}{20\times 85}+0.024\right)-294$$

Use the distributive property to multiply 2363.85 by x-263.

$$-x=\left(2363.85x-621692.55+4.9712\times 85\left(x-273\right)\right)\left(\frac{1}{20\times 85}+0.024\right)-294$$

Multiply 4.9712 and 85 to get 422.552.

$$-x=\left(2363.85x-621692.55+422.552\left(x-273\right)\right)\left(\frac{1}{20\times 85}+0.024\right)-294$$

Use the distributive property to multiply 422.552 by x-273.

$$-x=\left(2363.85x-621692.55+422.552x-115356.696\right)\left(\frac{1}{20\times 85}+0.024\right)-294$$

Combine 2363.85x and 422.552x to get 2786.402x.

$$-x=\left(2786.402x-621692.55-115356.696\right)\left(\frac{1}{20\times 85}+0.024\right)-294$$

Subtract 115356.696 from -621692.55 to get -737049.246.

$$-x=\left(2786.402x-737049.246\right)\left(\frac{1}{20\times 85}+0.024\right)-294$$

Multiply 20 and 85 to get 1700.

$$-x=\left(2786.402x-737049.246\right)\left(\frac{1}{1700}+0.024\right)-294$$

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.

$$-x=\left(2786.402x-737049.246\right)\left(\frac{1}{1700}+\frac{3}{125}\right)-294$$

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

$$-x=\left(2786.402x-737049.246\right)\left(\frac{5}{8500}+\frac{204}{8500}\right)-294$$

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

$$-x=\left(2786.402x-737049.246\right)\times \frac{5+204}{8500}-294$$

Add 5 and 204 to get 209.

$$-x=\left(2786.402x-737049.246\right)\times \frac{209}{8500}-294$$

Use the distributive property to multiply 2786.402x-737049.246 by \frac{209}{8500}.

$$-x=2786.402x\times \frac{209}{8500}-737049.246\times \frac{209}{8500}-294$$

Convert decimal number 2786.402 to fraction \frac{2786402}{1000}. Reduce the fraction \frac{2786402}{1000} to lowest terms by extracting and canceling out 2.

$$-x=\frac{1393201}{500}x\times \frac{209}{8500}-737049.246\times \frac{209}{8500}-294$$

Multiply \frac{1393201}{500} times \frac{209}{8500} by multiplying numerator times numerator and denominator times denominator.

$$-x=\frac{1393201\times 209}{500\times 8500}x-737049.246\times \frac{209}{8500}-294$$

Do the multiplications in the fraction \frac{1393201\times 209}{500\times 8500}.

$$-x=\frac{291179009}{4250000}x-737049.246\times \frac{209}{8500}-294$$

Reduce the fraction \frac{291179009}{4250000} to lowest terms by extracting and canceling out 17.

$$-x=\frac{17128177}{250000}x-737049.246\times \frac{209}{8500}-294$$

Convert decimal number -737049.246 to fraction -\frac{737049246}{1000}. Reduce the fraction -\frac{737049246}{1000} to lowest terms by extracting and canceling out 2.

$$-x=\frac{17128177}{250000}x-\frac{368524623}{500}\times \frac{209}{8500}-294$$

Multiply -\frac{368524623}{500} times \frac{209}{8500} by multiplying numerator times numerator and denominator times denominator.

$$-x=\frac{17128177}{250000}x+\frac{-368524623\times 209}{500\times 8500}-294$$

Do the multiplications in the fraction \frac{-368524623\times 209}{500\times 8500}.

$$-x=\frac{17128177}{250000}x+\frac{-77021646207}{4250000}-294$$

Reduce the fraction \frac{-77021646207}{4250000} to lowest terms by extracting and canceling out 17.

$$-x=\frac{17128177}{250000}x-\frac{4530685071}{250000}-294$$

Convert 294 to fraction \frac{73500000}{250000}.

$$-x=\frac{17128177}{250000}x-\frac{4530685071}{250000}-\frac{73500000}{250000}$$

Since -\frac{4530685071}{250000} and \frac{73500000}{250000} have the same denominator, subtract them by subtracting their numerators.

$$-x=\frac{17128177}{250000}x+\frac{-4530685071-73500000}{250000}$$

Subtract 73500000 from -4530685071 to get -4604185071.

$$-x=\frac{17128177}{250000}x-\frac{4604185071}{250000}$$

Subtract \frac{17128177}{250000}x from both sides.

$$-x-\frac{17128177}{250000}x=-\frac{4604185071}{250000}$$

Combine -x and -\frac{17128177}{250000}x to get -\frac{17378177}{250000}x.

$$-\frac{17378177}{250000}x=-\frac{4604185071}{250000}$$

Multiply both sides by -\frac{250000}{17378177}, the reciprocal of -\frac{17378177}{250000}.

$$x=-\frac{4604185071}{250000}\left(-\frac{250000}{17378177}\right)$$

Multiply -\frac{4604185071}{250000} times -\frac{250000}{17378177} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-4604185071\left(-250000\right)}{250000\times 17378177}$$

Do the multiplications in the fraction \frac{-4604185071\left(-250000\right)}{250000\times 17378177}.

$$x=\frac{1151046267750000}{4344544250000}$$

Reduce the fraction \frac{1151046267750000}{4344544250000} to lowest terms by extracting and canceling out 250000.

$$x=\frac{4604185071}{17378177}$$