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\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}=0.5
Reduce the fraction \frac{28}{48} to lowest terms by extracting and canceling out 4.
\left(\frac{7}{12}+\frac{245}{500}+\frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}=0.5
Expand \frac{24.5}{50} by multiplying both numerator and the denominator by 10.
\left(\frac{7}{12}+\frac{49}{100}+\frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}=0.5
Reduce the fraction \frac{245}{500} to lowest terms by extracting and canceling out 5.
\left(\frac{175}{300}+\frac{147}{300}+\frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}=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+147}{300}+\frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}=0.5
Since \frac{175}{300} and \frac{147}{300} have the same denominator, add them by adding their numerators.
\left(\frac{322}{300}+\frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}=0.5
Add 175 and 147 to get 322.
\left(\frac{161}{150}+\frac{x}{48+52}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}=0.5
Reduce the fraction \frac{322}{300} to lowest terms by extracting and canceling out 2.
\left(\frac{161}{150}+\frac{x}{100}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}=0.5
Add 48 and 52 to get 100.
\left(\frac{161\times 2}{300}+\frac{3x}{300}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}=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}.
\frac{161\times 2+3x}{300}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}=0.5
Since \frac{161\times 2}{300} and \frac{3x}{300} have the same denominator, add them by adding their numerators.
\frac{322+3x}{300}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}=0.5
Do the multiplications in 161\times 2+3x.
\frac{322+3x}{300}\times 0.1+\frac{4}{5}\times 0.15+\frac{15}{30}=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 \left(\frac{3}{20}\right)+\frac{15}{30}=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\times 3}{5\times 20}+\frac{15}{30}=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{12}{100}+\frac{15}{30}=0.5
Do the multiplications in the fraction \frac{4\times 3}{5\times 20}.
\frac{322+3x}{300}\times 0.1+\frac{3}{25}+\frac{15}{30}=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{1}{2}=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{6}{50}+\frac{25}{50}=0.5
Least common multiple of 25 and 2 is 50. Convert \frac{3}{25} and \frac{1}{2} to fractions with denominator 50.
\frac{322+3x}{300}\times 0.1+\frac{6+25}{50}=0.5
Since \frac{6}{50} and \frac{25}{50} have the same denominator, add them by adding their numerators.
\frac{322+3x}{300}\times 0.1+\frac{31}{50}=0.5
Add 6 and 25 to get 31.
\left(\frac{161}{150}+\frac{1}{100}x\right)\times 0.1+\frac{31}{50}=0.5
Divide each term of 322+3x by 300 to get \frac{161}{150}+\frac{1}{100}x.
\frac{161}{150}\times 0.1+\frac{1}{100}x\times 0.1+\frac{31}{50}=0.5
Use the distributive property to multiply \frac{161}{150}+\frac{1}{100}x by 0.1.
\frac{161}{150}\times \left(\frac{1}{10}\right)+\frac{1}{100}x\times 0.1+\frac{31}{50}=0.5
Convert decimal number 0.1 to fraction \frac{1}{10}.
\frac{161\times 1}{150\times 10}+\frac{1}{100}x\times 0.1+\frac{31}{50}=0.5
Multiply \frac{161}{150} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.
\frac{161}{1500}+\frac{1}{100}x\times 0.1+\frac{31}{50}=0.5
Do the multiplications in the fraction \frac{161\times 1}{150\times 10}.
\frac{161}{1500}+\frac{1}{100}x\times \left(\frac{1}{10}\right)+\frac{31}{50}=0.5
Convert decimal number 0.1 to fraction \frac{1}{10}.
\frac{161}{1500}+\frac{1\times 1}{100\times 10}x+\frac{31}{50}=0.5
Multiply \frac{1}{100} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.
\frac{161}{1500}+\frac{1}{1000}x+\frac{31}{50}=0.5
Do the multiplications in the fraction \frac{1\times 1}{100\times 10}.
\frac{161}{1500}+\frac{1}{1000}x+\frac{930}{1500}=0.5
Least common multiple of 1500 and 50 is 1500. Convert \frac{161}{1500} and \frac{31}{50} to fractions with denominator 1500.
\frac{161+930}{1500}+\frac{1}{1000}x=0.5
Since \frac{161}{1500} and \frac{930}{1500} have the same denominator, add them by adding their numerators.
\frac{1091}{1500}+\frac{1}{1000}x=0.5
Add 161 and 930 to get 1091.
\frac{1}{1000}x=0.5-\frac{1091}{1500}
Subtract \frac{1091}{1500} from both sides.
\frac{1}{1000}x=\frac{1}{2}-\frac{1091}{1500}
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{750}{1500}-\frac{1091}{1500}
Least common multiple of 2 and 1500 is 1500. Convert \frac{1}{2} and \frac{1091}{1500} to fractions with denominator 1500.
\frac{1}{1000}x=\frac{750-1091}{1500}
Since \frac{750}{1500} and \frac{1091}{1500} have the same denominator, subtract them by subtracting their numerators.
\frac{1}{1000}x=-\frac{341}{1500}
Subtract 1091 from 750 to get -341.
x=-\frac{341}{1500}\times 1000
Multiply both sides by 1000, the reciprocal of \frac{1}{1000}.
x=\frac{-341\times 1000}{1500}
Express -\frac{341}{1500}\times 1000 as a single fraction.
x=\frac{-341000}{1500}
Multiply -341 and 1000 to get -341000.
x=-\frac{682}{3}
Reduce the fraction \frac{-341000}{1500} to lowest terms by extracting and canceling out 500.