Solve (0.008-x)div0.04=((0.027-x)div0.09)*(8div27)

$$(0.008-x) \div 0.04=((0.027-x) \div 0.09) \times (8 \div 27)$$

Solve for x

$$x=\frac{27}{5275}\approx 0.005118483$$

Steps for Solving Linear Equation

Divide each term of 0.008-x by 0.04 to get \frac{0.008}{0.04}+\frac{-x}{0.04}.

$$\frac{0.008}{0.04}+\frac{-x}{0.04}=\frac{0.027-x}{0.09}\times \frac{8}{27}$$

Expand \frac{0.008}{0.04} by multiplying both numerator and the denominator by 1000.

$$\frac{8}{40}+\frac{-x}{0.04}=\frac{0.027-x}{0.09}\times \frac{8}{27}$$

Reduce the fraction \frac{8}{40} to lowest terms by extracting and canceling out 8.

$$\frac{1}{5}+\frac{-x}{0.04}=\frac{0.027-x}{0.09}\times \frac{8}{27}$$

Divide -x by 0.04 to get -25x.

$$\frac{1}{5}-25x=\frac{0.027-x}{0.09}\times \frac{8}{27}$$

Divide each term of 0.027-x by 0.09 to get \frac{0.027}{0.09}+\frac{-x}{0.09}.

$$\frac{1}{5}-25x=\left(\frac{0.027}{0.09}+\frac{-x}{0.09}\right)\times \frac{8}{27}$$

Expand \frac{0.027}{0.09} by multiplying both numerator and the denominator by 1000.

$$\frac{1}{5}-25x=\left(\frac{27}{90}+\frac{-x}{0.09}\right)\times \frac{8}{27}$$

Reduce the fraction \frac{27}{90} to lowest terms by extracting and canceling out 9.

$$\frac{1}{5}-25x=\left(\frac{3}{10}+\frac{-x}{0.09}\right)\times \frac{8}{27}$$

Divide -x by 0.09 to get -\frac{100}{9}x.

$$\frac{1}{5}-25x=\left(\frac{3}{10}-\frac{100}{9}x\right)\times \frac{8}{27}$$

Use the distributive property to multiply \frac{3}{10}-\frac{100}{9}x by \frac{8}{27}.

$$\frac{1}{5}-25x=\frac{3}{10}\times \frac{8}{27}-\frac{100}{9}x\times \frac{8}{27}$$

Multiply \frac{3}{10} times \frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{5}-25x=\frac{3\times 8}{10\times 27}-\frac{100}{9}x\times \frac{8}{27}$$

Do the multiplications in the fraction \frac{3\times 8}{10\times 27}.

$$\frac{1}{5}-25x=\frac{24}{270}-\frac{100}{9}x\times \frac{8}{27}$$

Reduce the fraction \frac{24}{270} to lowest terms by extracting and canceling out 6.

$$\frac{1}{5}-25x=\frac{4}{45}-\frac{100}{9}x\times \frac{8}{27}$$

Multiply -\frac{100}{9} times \frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{5}-25x=\frac{4}{45}+\frac{-100\times 8}{9\times 27}x$$

Do the multiplications in the fraction \frac{-100\times 8}{9\times 27}.

$$\frac{1}{5}-25x=\frac{4}{45}+\frac{-800}{243}x$$

Fraction \frac{-800}{243} can be rewritten as -\frac{800}{243} by extracting the negative sign.

$$\frac{1}{5}-25x=\frac{4}{45}-\frac{800}{243}x$$

Add \frac{800}{243}x to both sides.

$$\frac{1}{5}-25x+\frac{800}{243}x=\frac{4}{45}$$

Combine -25x and \frac{800}{243}x to get -\frac{5275}{243}x.

$$\frac{1}{5}-\frac{5275}{243}x=\frac{4}{45}$$

Subtract \frac{1}{5} from both sides.

$$-\frac{5275}{243}x=\frac{4}{45}-\frac{1}{5}$$

Least common multiple of 45 and 5 is 45. Convert \frac{4}{45} and \frac{1}{5} to fractions with denominator 45.

$$-\frac{5275}{243}x=\frac{4}{45}-\frac{9}{45}$$

Since \frac{4}{45} and \frac{9}{45} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5275}{243}x=\frac{4-9}{45}$$

Subtract 9 from 4 to get -5.

$$-\frac{5275}{243}x=\frac{-5}{45}$$

Reduce the fraction \frac{-5}{45} to lowest terms by extracting and canceling out 5.

$$-\frac{5275}{243}x=-\frac{1}{9}$$

Multiply both sides by -\frac{243}{5275}, the reciprocal of -\frac{5275}{243}.

$$x=-\frac{1}{9}\left(-\frac{243}{5275}\right)$$

Multiply -\frac{1}{9} times -\frac{243}{5275} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-\left(-243\right)}{9\times 5275}$$

Do the multiplications in the fraction \frac{-\left(-243\right)}{9\times 5275}.

$$x=\frac{243}{47475}$$

Reduce the fraction \frac{243}{47475} to lowest terms by extracting and canceling out 9.

$$x=\frac{27}{5275}$$