Solve .1(.94)+.25(18.5div25+.01)+.25(6div16+.02)+.4x=.7

$$.1(.94)+.25(18.5 \div 25+.01)+.25(6 \div 16+.02)+.4x=.7$$

Solve for x

$$x=0.799375$$

Steps for Solving Linear Equation

Multiply 0.1 and 0.94 to get 0.094.

$$0.094+0.25\left(\frac{18.5}{25}+0.01\right)+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

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

$$0.094+0.25\left(\frac{185}{250}+0.01\right)+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

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

$$0.094+0.25\left(\frac{37}{50}+0.01\right)+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Convert decimal number 0.01 to fraction \frac{1}{100}.

$$0.094+0.25\left(\frac{37}{50}+\frac{1}{100}\right)+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Least common multiple of 50 and 100 is 100. Convert \frac{37}{50} and \frac{1}{100} to fractions with denominator 100.

$$0.094+0.25\left(\frac{74}{100}+\frac{1}{100}\right)+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Since \frac{74}{100} and \frac{1}{100} have the same denominator, add them by adding their numerators.

$$0.094+0.25\times \frac{74+1}{100}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Add 74 and 1 to get 75.

$$0.094+0.25\times \frac{75}{100}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$0.094+0.25\times \frac{3}{4}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

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.

$$0.094+\frac{1}{4}\times \frac{3}{4}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Multiply \frac{1}{4} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$0.094+\frac{1\times 3}{4\times 4}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Do the multiplications in the fraction \frac{1\times 3}{4\times 4}.

$$0.094+\frac{3}{16}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

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.

$$\frac{47}{500}+\frac{3}{16}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Least common multiple of 500 and 16 is 2000. Convert \frac{47}{500} and \frac{3}{16} to fractions with denominator 2000.

$$\frac{188}{2000}+\frac{375}{2000}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Since \frac{188}{2000} and \frac{375}{2000} have the same denominator, add them by adding their numerators.

$$\frac{188+375}{2000}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Add 188 and 375 to get 563.

$$\frac{563}{2000}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

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

$$\frac{563}{2000}+0.25\left(\frac{3}{8}+0.02\right)+0.4x=0.7$$

Convert decimal number 0.02 to fraction \frac{2}{100}. Reduce the fraction \frac{2}{100} to lowest terms by extracting and canceling out 2.

$$\frac{563}{2000}+0.25\left(\frac{3}{8}+\frac{1}{50}\right)+0.4x=0.7$$

Least common multiple of 8 and 50 is 200. Convert \frac{3}{8} and \frac{1}{50} to fractions with denominator 200.

$$\frac{563}{2000}+0.25\left(\frac{75}{200}+\frac{4}{200}\right)+0.4x=0.7$$

Since \frac{75}{200} and \frac{4}{200} have the same denominator, add them by adding their numerators.

$$\frac{563}{2000}+0.25\times \frac{75+4}{200}+0.4x=0.7$$

Add 75 and 4 to get 79.

$$\frac{563}{2000}+0.25\times \frac{79}{200}+0.4x=0.7$$

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.

$$\frac{563}{2000}+\frac{1}{4}\times \frac{79}{200}+0.4x=0.7$$

Multiply \frac{1}{4} times \frac{79}{200} by multiplying numerator times numerator and denominator times denominator.

$$\frac{563}{2000}+\frac{1\times 79}{4\times 200}+0.4x=0.7$$

Do the multiplications in the fraction \frac{1\times 79}{4\times 200}.

$$\frac{563}{2000}+\frac{79}{800}+0.4x=0.7$$

Least common multiple of 2000 and 800 is 4000. Convert \frac{563}{2000} and \frac{79}{800} to fractions with denominator 4000.

$$\frac{1126}{4000}+\frac{395}{4000}+0.4x=0.7$$

Since \frac{1126}{4000} and \frac{395}{4000} have the same denominator, add them by adding their numerators.

$$\frac{1126+395}{4000}+0.4x=0.7$$

Add 1126 and 395 to get 1521.

$$\frac{1521}{4000}+0.4x=0.7$$

Subtract \frac{1521}{4000} from both sides.

$$0.4x=0.7-\frac{1521}{4000}$$

Convert decimal number 0.7 to fraction \frac{7}{10}.

$$0.4x=\frac{7}{10}-\frac{1521}{4000}$$

Least common multiple of 10 and 4000 is 4000. Convert \frac{7}{10} and \frac{1521}{4000} to fractions with denominator 4000.

$$0.4x=\frac{2800}{4000}-\frac{1521}{4000}$$

Since \frac{2800}{4000} and \frac{1521}{4000} have the same denominator, subtract them by subtracting their numerators.

$$0.4x=\frac{2800-1521}{4000}$$

Subtract 1521 from 2800 to get 1279.

$$0.4x=\frac{1279}{4000}$$

Divide both sides by 0.4.

$$x=\frac{\frac{1279}{4000}}{0.4}$$

Express \frac{\frac{1279}{4000}}{0.4} as a single fraction.

$$x=\frac{1279}{4000\times 0.4}$$

Multiply 4000 and 0.4 to get 1600.

$$x=\frac{1279}{1600}$$