Solve .1(.94)+.25(18.5div25+.6)+.25(6div16+.075)+.4x=.8

$$.1(.94)+.25(18.5 \div 25+.6)+.25(6 \div 16+.075)+.4x=.8$$

Solve for x

$$x=0.64625$$

Steps for Solving Linear Equation

Multiply 0.1 and 0.94 to get 0.094.

$$0.094+0.25\left(\frac{18.5}{25}+0.6\right)+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Expand \frac{18.5}{25} by multiplying both numerator and the denominator by 10.

$$0.094+0.25\left(\frac{185}{250}+0.6\right)+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Reduce the fraction \frac{185}{250} to lowest terms by extracting and canceling out 5.

$$0.094+0.25\left(\frac{37}{50}+0.6\right)+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Convert decimal number 0.6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$0.094+0.25\left(\frac{37}{50}+\frac{3}{5}\right)+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Least common multiple of 50 and 5 is 50. Convert \frac{37}{50} and \frac{3}{5} to fractions with denominator 50.

$$0.094+0.25\left(\frac{37}{50}+\frac{30}{50}\right)+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Since \frac{37}{50} and \frac{30}{50} have the same denominator, add them by adding their numerators.

$$0.094+0.25\times \frac{37+30}{50}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Add 37 and 30 to get 67.

$$0.094+0.25\times \frac{67}{50}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Convert decimal number 0.25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$0.094+\frac{1}{4}\times \frac{67}{50}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Multiply \frac{1}{4} times \frac{67}{50} by multiplying numerator times numerator and denominator times denominator.

$$0.094+\frac{1\times 67}{4\times 50}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Do the multiplications in the fraction \frac{1\times 67}{4\times 50}.

$$0.094+\frac{67}{200}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Convert decimal number 0.094 to fraction \frac{94}{1000}. Reduce the fraction \frac{94}{1000} to lowest terms by extracting and canceling out 2.

$$\frac{47}{500}+\frac{67}{200}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Least common multiple of 500 and 200 is 1000. Convert \frac{47}{500} and \frac{67}{200} to fractions with denominator 1000.

$$\frac{94}{1000}+\frac{335}{1000}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Since \frac{94}{1000} and \frac{335}{1000} have the same denominator, add them by adding their numerators.

$$\frac{94+335}{1000}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Add 94 and 335 to get 429.

$$\frac{429}{1000}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.8$$

Reduce the fraction \frac{6}{16} to lowest terms by extracting and canceling out 2.

$$\frac{429}{1000}+0.25\left(\frac{3}{8}+0.075\right)+0.4x=0.8$$

Convert decimal number 0.075 to fraction \frac{75}{1000}. Reduce the fraction \frac{75}{1000} to lowest terms by extracting and canceling out 25.

$$\frac{429}{1000}+0.25\left(\frac{3}{8}+\frac{3}{40}\right)+0.4x=0.8$$

Least common multiple of 8 and 40 is 40. Convert \frac{3}{8} and \frac{3}{40} to fractions with denominator 40.

$$\frac{429}{1000}+0.25\left(\frac{15}{40}+\frac{3}{40}\right)+0.4x=0.8$$

Since \frac{15}{40} and \frac{3}{40} have the same denominator, add them by adding their numerators.

$$\frac{429}{1000}+0.25\times \frac{15+3}{40}+0.4x=0.8$$

Add 15 and 3 to get 18.

$$\frac{429}{1000}+0.25\times \frac{18}{40}+0.4x=0.8$$

Reduce the fraction \frac{18}{40} to lowest terms by extracting and canceling out 2.

$$\frac{429}{1000}+0.25\times \frac{9}{20}+0.4x=0.8$$

Convert decimal number 0.25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{429}{1000}+\frac{1}{4}\times \frac{9}{20}+0.4x=0.8$$

Multiply \frac{1}{4} times \frac{9}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{429}{1000}+\frac{1\times 9}{4\times 20}+0.4x=0.8$$

Do the multiplications in the fraction \frac{1\times 9}{4\times 20}.

$$\frac{429}{1000}+\frac{9}{80}+0.4x=0.8$$

Least common multiple of 1000 and 80 is 2000. Convert \frac{429}{1000} and \frac{9}{80} to fractions with denominator 2000.

$$\frac{858}{2000}+\frac{225}{2000}+0.4x=0.8$$

Since \frac{858}{2000} and \frac{225}{2000} have the same denominator, add them by adding their numerators.

$$\frac{858+225}{2000}+0.4x=0.8$$

Add 858 and 225 to get 1083.

$$\frac{1083}{2000}+0.4x=0.8$$

Subtract \frac{1083}{2000} from both sides.

$$0.4x=0.8-\frac{1083}{2000}$$

Convert decimal number 0.8 to fraction \frac{8}{10}. Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$0.4x=\frac{4}{5}-\frac{1083}{2000}$$

Least common multiple of 5 and 2000 is 2000. Convert \frac{4}{5} and \frac{1083}{2000} to fractions with denominator 2000.

$$0.4x=\frac{1600}{2000}-\frac{1083}{2000}$$

Since \frac{1600}{2000} and \frac{1083}{2000} have the same denominator, subtract them by subtracting their numerators.

$$0.4x=\frac{1600-1083}{2000}$$

Subtract 1083 from 1600 to get 517.

$$0.4x=\frac{517}{2000}$$

Divide both sides by 0.4.

$$x=\frac{\frac{517}{2000}}{0.4}$$

Express \frac{\frac{517}{2000}}{0.4} as a single fraction.

$$x=\frac{517}{2000\times 0.4}$$

Multiply 2000 and 0.4 to get 800.

$$x=\frac{517}{800}$$