Solve .1(.94)+.25(18.5div25+.09)+.25(6div16+.075)+.4x=.7

$$.1(.94)+.25(18.5 \div 25+.09)+.25(6 \div 16+.075)+.4x=.7$$

Solve for x

$$x=0.715$$

Steps for Solving Linear Equation

Multiply 0.1 and 0.94 to get 0.094.

$$0.094+0.25\left(\frac{18.5}{25}+0.09\right)+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

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

$$0.094+0.25\left(\frac{185}{250}+0.09\right)+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

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

$$0.094+0.25\left(\frac{37}{50}+0.09\right)+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

Convert decimal number 0.09 to fraction \frac{9}{100}.

$$0.094+0.25\left(\frac{37}{50}+\frac{9}{100}\right)+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

Least common multiple of 50 and 100 is 100. Convert \frac{37}{50} and \frac{9}{100} to fractions with denominator 100.

$$0.094+0.25\left(\frac{74}{100}+\frac{9}{100}\right)+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

Since \frac{74}{100} and \frac{9}{100} have the same denominator, add them by adding their numerators.

$$0.094+0.25\times \frac{74+9}{100}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

Add 74 and 9 to get 83.

$$0.094+0.25\times \frac{83}{100}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

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.

$$0.094+\frac{1}{4}\times \frac{83}{100}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

Multiply \frac{1}{4} times \frac{83}{100} by multiplying numerator times numerator and denominator times denominator.

$$0.094+\frac{1\times 83}{4\times 100}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

Do the multiplications in the fraction \frac{1\times 83}{4\times 100}.

$$0.094+\frac{83}{400}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

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.

$$\frac{47}{500}+\frac{83}{400}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

Least common multiple of 500 and 400 is 2000. Convert \frac{47}{500} and \frac{83}{400} to fractions with denominator 2000.

$$\frac{188}{2000}+\frac{415}{2000}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

Since \frac{188}{2000} and \frac{415}{2000} have the same denominator, add them by adding their numerators.

$$\frac{188+415}{2000}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

Add 188 and 415 to get 603.

$$\frac{603}{2000}+0.25\left(\frac{6}{16}+0.075\right)+0.4x=0.7$$

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

$$\frac{603}{2000}+0.25\left(\frac{3}{8}+0.075\right)+0.4x=0.7$$

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.

$$\frac{603}{2000}+0.25\left(\frac{3}{8}+\frac{3}{40}\right)+0.4x=0.7$$

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

$$\frac{603}{2000}+0.25\left(\frac{15}{40}+\frac{3}{40}\right)+0.4x=0.7$$

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

$$\frac{603}{2000}+0.25\times \frac{15+3}{40}+0.4x=0.7$$

Add 15 and 3 to get 18.

$$\frac{603}{2000}+0.25\times \frac{18}{40}+0.4x=0.7$$

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

$$\frac{603}{2000}+0.25\times \frac{9}{20}+0.4x=0.7$$

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.

$$\frac{603}{2000}+\frac{1}{4}\times \frac{9}{20}+0.4x=0.7$$

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

$$\frac{603}{2000}+\frac{1\times 9}{4\times 20}+0.4x=0.7$$

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

$$\frac{603}{2000}+\frac{9}{80}+0.4x=0.7$$

Least common multiple of 2000 and 80 is 2000. Convert \frac{603}{2000} and \frac{9}{80} to fractions with denominator 2000.

$$\frac{603}{2000}+\frac{225}{2000}+0.4x=0.7$$

Since \frac{603}{2000} and \frac{225}{2000} have the same denominator, add them by adding their numerators.

$$\frac{603+225}{2000}+0.4x=0.7$$

Add 603 and 225 to get 828.

$$\frac{828}{2000}+0.4x=0.7$$

Reduce the fraction \frac{828}{2000} to lowest terms by extracting and canceling out 4.

$$\frac{207}{500}+0.4x=0.7$$

Subtract \frac{207}{500} from both sides.

$$0.4x=0.7-\frac{207}{500}$$

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

$$0.4x=\frac{7}{10}-\frac{207}{500}$$

Least common multiple of 10 and 500 is 500. Convert \frac{7}{10} and \frac{207}{500} to fractions with denominator 500.

$$0.4x=\frac{350}{500}-\frac{207}{500}$$

Since \frac{350}{500} and \frac{207}{500} have the same denominator, subtract them by subtracting their numerators.

$$0.4x=\frac{350-207}{500}$$

Subtract 207 from 350 to get 143.

$$0.4x=\frac{143}{500}$$

Divide both sides by 0.4.

$$x=\frac{\frac{143}{500}}{0.4}$$

Express \frac{\frac{143}{500}}{0.4} as a single fraction.

$$x=\frac{143}{500\times 0.4}$$

Multiply 500 and 0.4 to get 200.

$$x=\frac{143}{200}$$