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\left(\frac{7}{12}+\frac{24.5}{50}\times \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{28}{48} to lowest terms by extracting and canceling out 4.
\left(\frac{7}{12}+\frac{245}{500}\times \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{49}{100}\times \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}\times \frac{x}{100}\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{7}{12}+\frac{49x}{100\times 100}\right)\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5
Multiply \frac{49}{100} times \frac{x}{100} by multiplying numerator times numerator and denominator times denominator.
\left(\frac{7\times 2500}{30000}+\frac{3\times 49x}{30000}\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 12 and 100\times 100 is 30000. Multiply \frac{7}{12} times \frac{2500}{2500}. Multiply \frac{49x}{100\times 100} times \frac{3}{3}.
\frac{7\times 2500+3\times 49x}{30000}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5
Since \frac{7\times 2500}{30000} and \frac{3\times 49x}{30000} have the same denominator, add them by adding their numerators.
\frac{17500+147x}{30000}\times 0.1+\frac{8}{10}\times 0.15+\frac{15}{30}\times 0.75=0.5
Do the multiplications in 7\times 2500+3\times 49x.
\frac{17500+147x}{30000}\times 0.1+\frac{4}{5}\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{17500+147x}{30000}\times 0.1+\frac{4}{5}\times \frac{3}{20}+\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{17500+147x}{30000}\times 0.1+\frac{4\times 3}{5\times 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{17500+147x}{30000}\times 0.1+\frac{12}{100}+\frac{15}{30}\times 0.75=0.5
Do the multiplications in the fraction \frac{4\times 3}{5\times 20}.
\frac{17500+147x}{30000}\times 0.1+\frac{3}{25}+\frac{15}{30}\times 0.75=0.5
Reduce the fraction \frac{12}{100} to lowest terms by extracting and canceling out 4.
\frac{17500+147x}{30000}\times 0.1+\frac{3}{25}+\frac{1}{2}\times 0.75=0.5
Reduce the fraction \frac{15}{30} to lowest terms by extracting and canceling out 15.
\frac{17500+147x}{30000}\times 0.1+\frac{3}{25}+\frac{1}{2}\times \frac{3}{4}=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{17500+147x}{30000}\times 0.1+\frac{3}{25}+\frac{1\times 3}{2\times 4}=0.5
Multiply \frac{1}{2} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.
\frac{17500+147x}{30000}\times 0.1+\frac{3}{25}+\frac{3}{8}=0.5
Do the multiplications in the fraction \frac{1\times 3}{2\times 4}.
\frac{17500+147x}{30000}\times 0.1+\frac{24}{200}+\frac{75}{200}=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{17500+147x}{30000}\times 0.1+\frac{24+75}{200}=0.5
Since \frac{24}{200} and \frac{75}{200} have the same denominator, add them by adding their numerators.
\frac{17500+147x}{30000}\times 0.1+\frac{99}{200}=0.5
Add 24 and 75 to get 99.
\left(\frac{7}{12}+\frac{49}{10000}x\right)\times 0.1+\frac{99}{200}=0.5
Divide each term of 17500+147x by 30000 to get \frac{7}{12}+\frac{49}{10000}x.
\frac{7}{12}\times 0.1+\frac{49}{10000}x\times 0.1+\frac{99}{200}=0.5
Use the distributive property to multiply \frac{7}{12}+\frac{49}{10000}x by 0.1.
\frac{7}{12}\times \frac{1}{10}+\frac{49}{10000}x\times 0.1+\frac{99}{200}=0.5
Convert decimal number 0.1 to fraction \frac{1}{10}.
\frac{7\times 1}{12\times 10}+\frac{49}{10000}x\times 0.1+\frac{99}{200}=0.5
Multiply \frac{7}{12} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.
\frac{7}{120}+\frac{49}{10000}x\times 0.1+\frac{99}{200}=0.5
Do the multiplications in the fraction \frac{7\times 1}{12\times 10}.
\frac{7}{120}+\frac{49}{10000}x\times \frac{1}{10}+\frac{99}{200}=0.5
Convert decimal number 0.1 to fraction \frac{1}{10}.
\frac{7}{120}+\frac{49\times 1}{10000\times 10}x+\frac{99}{200}=0.5
Multiply \frac{49}{10000} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.
\frac{7}{120}+\frac{49}{100000}x+\frac{99}{200}=0.5
Do the multiplications in the fraction \frac{49\times 1}{10000\times 10}.
\frac{35}{600}+\frac{49}{100000}x+\frac{297}{600}=0.5
Least common multiple of 120 and 200 is 600. Convert \frac{7}{120} and \frac{99}{200} to fractions with denominator 600.
\frac{35+297}{600}+\frac{49}{100000}x=0.5
Since \frac{35}{600} and \frac{297}{600} have the same denominator, add them by adding their numerators.
\frac{332}{600}+\frac{49}{100000}x=0.5
Add 35 and 297 to get 332.
\frac{83}{150}+\frac{49}{100000}x=0.5
Reduce the fraction \frac{332}{600} to lowest terms by extracting and canceling out 4.
\frac{49}{100000}x=0.5-\frac{83}{150}
Subtract \frac{83}{150} from both sides.
\frac{49}{100000}x=\frac{1}{2}-\frac{83}{150}
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{49}{100000}x=\frac{75}{150}-\frac{83}{150}
Least common multiple of 2 and 150 is 150. Convert \frac{1}{2} and \frac{83}{150} to fractions with denominator 150.
\frac{49}{100000}x=\frac{75-83}{150}
Since \frac{75}{150} and \frac{83}{150} have the same denominator, subtract them by subtracting their numerators.
\frac{49}{100000}x=\frac{-8}{150}
Subtract 83 from 75 to get -8.
\frac{49}{100000}x=-\frac{4}{75}
Reduce the fraction \frac{-8}{150} to lowest terms by extracting and canceling out 2.
x=-\frac{4}{75}\times \frac{100000}{49}
Multiply both sides by \frac{100000}{49}, the reciprocal of \frac{49}{100000}.
x=\frac{-4\times 100000}{75\times 49}
Multiply -\frac{4}{75} times \frac{100000}{49} by multiplying numerator times numerator and denominator times denominator.
x=\frac{-400000}{3675}
Do the multiplications in the fraction \frac{-4\times 100000}{75\times 49}.
x=-\frac{16000}{147}
Reduce the fraction \frac{-400000}{3675} to lowest terms by extracting and canceling out 25.