Solve (28/48+24.5/50+x/48+52)*0.1+8/10*0.15+frac{15}{30}*0.75=0.5

$$( \frac{ 28 }{ 48 } + \frac{ 24.5 }{ 50 } + \frac{ x }{ 48+52 } ) \times 0.1+ \frac{ 8 }{ 10 } \times 0.15+ \frac{ 15 }{ 30 } \times 0.75=0.5$$

Solve for x

$$x = -\frac{307}{3} = -102\frac{1}{3} \approx -102.333333333$$

Steps for Solving Linear Equation

Reduce the fraction \frac{28}{48} to lowest terms by extracting and canceling out 4.

$$\left(\frac{7}{12}+\frac{24.5}{50}+\frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Expand \frac{24.5}{50} by multiplying both numerator and the denominator by 10.

$$\left(\frac{7}{12}+\frac{245}{500}+\frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Reduce the fraction \frac{245}{500} to lowest terms by extracting and canceling out 5.

$$\left(\frac{7}{12}+\frac{49}{100}+\frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Least common multiple of 12 and 100 is 300. Convert \frac{7}{12} and \frac{49}{100} to fractions with denominator 300.

$$\left(\frac{175}{300}+\frac{147}{300}+\frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Since \frac{175}{300} and \frac{147}{300} have the same denominator, add them by adding their numerators.

$$\left(\frac{175+147}{300}+\frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Add 175 and 147 to get 322.

$$\left(\frac{322}{300}+\frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Reduce the fraction \frac{322}{300} to lowest terms by extracting and canceling out 2.

$$\left(\frac{161}{150}+\frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Add 48 and 52 to get 100.

$$\left(\frac{161}{150}+\frac{x}{100}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 150 and 100 is 300. Multiply \frac{161}{150} times \frac{2}{2}. Multiply \frac{x}{100} times \frac{3}{3}.

$$\left(\frac{161\times 2}{300}+\frac{3x}{300}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Since \frac{161\times 2}{300} and \frac{3x}{300} have the same denominator, add them by adding their numerators.

$$\frac{161\times 2+3x}{300}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Do the multiplications in 161\times 2+3x.

$$\frac{322+3x}{300}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

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

$$\frac{322+3x}{300}\times 0.1+\frac{4}{5}\times 0.15+\frac{15}{30}\times 0.75=0.5$$

Convert decimal number 0.15 to fraction \frac{15}{100}. Reduce the fraction \frac{15}{100} to lowest terms by extracting and canceling out 5.

$$\frac{322+3x}{300}\times 0.1+\frac{4}{5}\times \frac{3}{20}+\frac{15}{30}\times 0.75=0.5$$

Multiply \frac{4}{5} times \frac{3}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{322+3x}{300}\times 0.1+\frac{4\times 3}{5\times 20}+\frac{15}{30}\times 0.75=0.5$$

Do the multiplications in the fraction \frac{4\times 3}{5\times 20}.

$$\frac{322+3x}{300}\times 0.1+\frac{12}{100}+\frac{15}{30}\times 0.75=0.5$$

Reduce the fraction \frac{12}{100} to lowest terms by extracting and canceling out 4.

$$\frac{322+3x}{300}\times 0.1+\frac{3}{25}+\frac{15}{30}\times 0.75=0.5$$

Reduce the fraction \frac{15}{30} to lowest terms by extracting and canceling out 15.

$$\frac{322+3x}{300}\times 0.1+\frac{3}{25}+\frac{1}{2}\times 0.75=0.5$$

Convert decimal number 0.75 to fraction \frac{75}{100}. Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{322+3x}{300}\times 0.1+\frac{3}{25}+\frac{1}{2}\times \frac{3}{4}=0.5$$

Multiply \frac{1}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{322+3x}{300}\times 0.1+\frac{3}{25}+\frac{1\times 3}{2\times 4}=0.5$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 4}.

$$\frac{322+3x}{300}\times 0.1+\frac{3}{25}+\frac{3}{8}=0.5$$

Least common multiple of 25 and 8 is 200. Convert \frac{3}{25} and \frac{3}{8} to fractions with denominator 200.

$$\frac{322+3x}{300}\times 0.1+\frac{24}{200}+\frac{75}{200}=0.5$$

Since \frac{24}{200} and \frac{75}{200} have the same denominator, add them by adding their numerators.

$$\frac{322+3x}{300}\times 0.1+\frac{24+75}{200}=0.5$$

Add 24 and 75 to get 99.

$$\frac{322+3x}{300}\times 0.1+\frac{99}{200}=0.5$$

Divide each term of 322+3x by 300 to get \frac{161}{150}+\frac{1}{100}x.

$$\left(\frac{161}{150}+\frac{1}{100}x\right)\times 0.1+\frac{99}{200}=0.5$$

Use the distributive property to multiply \frac{161}{150}+\frac{1}{100}x by 0.1.

$$\frac{161}{150}\times 0.1+\frac{1}{100}x\times 0.1+\frac{99}{200}=0.5$$

Convert decimal number 0.1 to fraction \frac{1}{10}.

$$\frac{161}{150}\times \frac{1}{10}+\frac{1}{100}x\times 0.1+\frac{99}{200}=0.5$$

Multiply \frac{161}{150} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{161\times 1}{150\times 10}+\frac{1}{100}x\times 0.1+\frac{99}{200}=0.5$$

Do the multiplications in the fraction \frac{161\times 1}{150\times 10}.

$$\frac{161}{1500}+\frac{1}{100}x\times 0.1+\frac{99}{200}=0.5$$

Convert decimal number 0.1 to fraction \frac{1}{10}.

$$\frac{161}{1500}+\frac{1}{100}x\times \frac{1}{10}+\frac{99}{200}=0.5$$

Multiply \frac{1}{100} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{161}{1500}+\frac{1\times 1}{100\times 10}x+\frac{99}{200}=0.5$$

Do the multiplications in the fraction \frac{1\times 1}{100\times 10}.

$$\frac{161}{1500}+\frac{1}{1000}x+\frac{99}{200}=0.5$$

Least common multiple of 1500 and 200 is 3000. Convert \frac{161}{1500} and \frac{99}{200} to fractions with denominator 3000.

$$\frac{322}{3000}+\frac{1}{1000}x+\frac{1485}{3000}=0.5$$

Since \frac{322}{3000} and \frac{1485}{3000} have the same denominator, add them by adding their numerators.

$$\frac{322+1485}{3000}+\frac{1}{1000}x=0.5$$

Add 322 and 1485 to get 1807.

$$\frac{1807}{3000}+\frac{1}{1000}x=0.5$$

Subtract \frac{1807}{3000} from both sides.

$$\frac{1}{1000}x=0.5-\frac{1807}{3000}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{1000}x=\frac{1}{2}-\frac{1807}{3000}$$

Least common multiple of 2 and 3000 is 3000. Convert \frac{1}{2} and \frac{1807}{3000} to fractions with denominator 3000.

$$\frac{1}{1000}x=\frac{1500}{3000}-\frac{1807}{3000}$$

Since \frac{1500}{3000} and \frac{1807}{3000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{1000}x=\frac{1500-1807}{3000}$$

Subtract 1807 from 1500 to get -307.

$$\frac{1}{1000}x=-\frac{307}{3000}$$

Multiply both sides by 1000, the reciprocal of \frac{1}{1000}.

$$x=-\frac{307}{3000}\times 1000$$

Express -\frac{307}{3000}\times 1000 as a single fraction.

$$x=\frac{-307\times 1000}{3000}$$

Multiply -307 and 1000 to get -307000.

$$x=\frac{-307000}{3000}$$

Reduce the fraction \frac{-307000}{3000} to lowest terms by extracting and canceling out 1000.

$$x=-\frac{307}{3}$$