Evaluate
\frac{b}{2}+\frac{152a}{15}+3
Expand
\frac{b}{2}+\frac{152a}{15}+3
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10a-2b+1-\frac{1}{3}\times 2a-\frac{1}{3}\left(-9\right)b-\frac{1}{10}\left(-20-8a+5b\right)
Use the distributive property to multiply -\frac{1}{3} by 2a-9b.
10a-2b+1+\frac{-2}{3}a-\frac{1}{3}\left(-9\right)b-\frac{1}{10}\left(-20-8a+5b\right)
Express -\frac{1}{3}\times 2 as a single fraction.
10a-2b+1-\frac{2}{3}a-\frac{1}{3}\left(-9\right)b-\frac{1}{10}\left(-20-8a+5b\right)
Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.
10a-2b+1-\frac{2}{3}a+\frac{-\left(-9\right)}{3}b-\frac{1}{10}\left(-20-8a+5b\right)
Express -\frac{1}{3}\left(-9\right) as a single fraction.
10a-2b+1-\frac{2}{3}a+\frac{9}{3}b-\frac{1}{10}\left(-20-8a+5b\right)
Multiply -1 and -9 to get 9.
10a-2b+1-\frac{2}{3}a+3b-\frac{1}{10}\left(-20-8a+5b\right)
Divide 9 by 3 to get 3.
\frac{28}{3}a-2b+1+3b-\frac{1}{10}\left(-20-8a+5b\right)
Combine 10a and -\frac{2}{3}a to get \frac{28}{3}a.
\frac{28}{3}a+b+1-\frac{1}{10}\left(-20-8a+5b\right)
Combine -2b and 3b to get b.
\frac{28}{3}a+b+1-\frac{1}{10}\left(-20\right)-\frac{1}{10}\left(-8\right)a-\frac{1}{10}\times 5b
Use the distributive property to multiply -\frac{1}{10} by -20-8a+5b.
\frac{28}{3}a+b+1+\frac{-\left(-20\right)}{10}-\frac{1}{10}\left(-8\right)a-\frac{1}{10}\times 5b
Express -\frac{1}{10}\left(-20\right) as a single fraction.
\frac{28}{3}a+b+1+\frac{20}{10}-\frac{1}{10}\left(-8\right)a-\frac{1}{10}\times 5b
Multiply -1 and -20 to get 20.
\frac{28}{3}a+b+1+2-\frac{1}{10}\left(-8\right)a-\frac{1}{10}\times 5b
Divide 20 by 10 to get 2.
\frac{28}{3}a+b+1+2+\frac{-\left(-8\right)}{10}a-\frac{1}{10}\times 5b
Express -\frac{1}{10}\left(-8\right) as a single fraction.
\frac{28}{3}a+b+1+2+\frac{8}{10}a-\frac{1}{10}\times 5b
Multiply -1 and -8 to get 8.
\frac{28}{3}a+b+1+2+\frac{4}{5}a-\frac{1}{10}\times 5b
Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.
\frac{28}{3}a+b+1+2+\frac{4}{5}a+\frac{-5}{10}b
Express -\frac{1}{10}\times 5 as a single fraction.
\frac{28}{3}a+b+1+2+\frac{4}{5}a-\frac{1}{2}b
Reduce the fraction \frac{-5}{10} to lowest terms by extracting and canceling out 5.
\frac{28}{3}a+b+3+\frac{4}{5}a-\frac{1}{2}b
Add 1 and 2 to get 3.
\frac{152}{15}a+b+3-\frac{1}{2}b
Combine \frac{28}{3}a and \frac{4}{5}a to get \frac{152}{15}a.
\frac{152}{15}a+\frac{1}{2}b+3
Combine b and -\frac{1}{2}b to get \frac{1}{2}b.
10a-2b+1-\frac{1}{3}\times 2a-\frac{1}{3}\left(-9\right)b-\frac{1}{10}\left(-20-8a+5b\right)
Use the distributive property to multiply -\frac{1}{3} by 2a-9b.
10a-2b+1+\frac{-2}{3}a-\frac{1}{3}\left(-9\right)b-\frac{1}{10}\left(-20-8a+5b\right)
Express -\frac{1}{3}\times 2 as a single fraction.
10a-2b+1-\frac{2}{3}a-\frac{1}{3}\left(-9\right)b-\frac{1}{10}\left(-20-8a+5b\right)
Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.
10a-2b+1-\frac{2}{3}a+\frac{-\left(-9\right)}{3}b-\frac{1}{10}\left(-20-8a+5b\right)
Express -\frac{1}{3}\left(-9\right) as a single fraction.
10a-2b+1-\frac{2}{3}a+\frac{9}{3}b-\frac{1}{10}\left(-20-8a+5b\right)
Multiply -1 and -9 to get 9.
10a-2b+1-\frac{2}{3}a+3b-\frac{1}{10}\left(-20-8a+5b\right)
Divide 9 by 3 to get 3.
\frac{28}{3}a-2b+1+3b-\frac{1}{10}\left(-20-8a+5b\right)
Combine 10a and -\frac{2}{3}a to get \frac{28}{3}a.
\frac{28}{3}a+b+1-\frac{1}{10}\left(-20-8a+5b\right)
Combine -2b and 3b to get b.
\frac{28}{3}a+b+1-\frac{1}{10}\left(-20\right)-\frac{1}{10}\left(-8\right)a-\frac{1}{10}\times 5b
Use the distributive property to multiply -\frac{1}{10} by -20-8a+5b.
\frac{28}{3}a+b+1+\frac{-\left(-20\right)}{10}-\frac{1}{10}\left(-8\right)a-\frac{1}{10}\times 5b
Express -\frac{1}{10}\left(-20\right) as a single fraction.
\frac{28}{3}a+b+1+\frac{20}{10}-\frac{1}{10}\left(-8\right)a-\frac{1}{10}\times 5b
Multiply -1 and -20 to get 20.
\frac{28}{3}a+b+1+2-\frac{1}{10}\left(-8\right)a-\frac{1}{10}\times 5b
Divide 20 by 10 to get 2.
\frac{28}{3}a+b+1+2+\frac{-\left(-8\right)}{10}a-\frac{1}{10}\times 5b
Express -\frac{1}{10}\left(-8\right) as a single fraction.
\frac{28}{3}a+b+1+2+\frac{8}{10}a-\frac{1}{10}\times 5b
Multiply -1 and -8 to get 8.
\frac{28}{3}a+b+1+2+\frac{4}{5}a-\frac{1}{10}\times 5b
Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.
\frac{28}{3}a+b+1+2+\frac{4}{5}a+\frac{-5}{10}b
Express -\frac{1}{10}\times 5 as a single fraction.
\frac{28}{3}a+b+1+2+\frac{4}{5}a-\frac{1}{2}b
Reduce the fraction \frac{-5}{10} to lowest terms by extracting and canceling out 5.
\frac{28}{3}a+b+3+\frac{4}{5}a-\frac{1}{2}b
Add 1 and 2 to get 3.
\frac{152}{15}a+b+3-\frac{1}{2}b
Combine \frac{28}{3}a and \frac{4}{5}a to get \frac{152}{15}a.
\frac{152}{15}a+\frac{1}{2}b+3
Combine b and -\frac{1}{2}b to get \frac{1}{2}b.
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Simultaneous equation
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Differentiation
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Limits
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