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x<\frac{3}{2}
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\frac{1}{11}\times 2x+\frac{1}{11}\left(-3\right)+\frac{1}{19}\left(3-2x\right)+\frac{2}{13}x<\frac{3}{13}
Use the distributive property to multiply \frac{1}{11} by 2x-3.
\frac{2}{11}x+\frac{1}{11}\left(-3\right)+\frac{1}{19}\left(3-2x\right)+\frac{2}{13}x<\frac{3}{13}
Multiply \frac{1}{11} and 2 to get \frac{2}{11}.
\frac{2}{11}x+\frac{-3}{11}+\frac{1}{19}\left(3-2x\right)+\frac{2}{13}x<\frac{3}{13}
Multiply \frac{1}{11} and -3 to get \frac{-3}{11}.
\frac{2}{11}x-\frac{3}{11}+\frac{1}{19}\left(3-2x\right)+\frac{2}{13}x<\frac{3}{13}
Fraction \frac{-3}{11} can be rewritten as -\frac{3}{11} by extracting the negative sign.
\frac{2}{11}x-\frac{3}{11}+\frac{1}{19}\times 3+\frac{1}{19}\left(-2\right)x+\frac{2}{13}x<\frac{3}{13}
Use the distributive property to multiply \frac{1}{19} by 3-2x.
\frac{2}{11}x-\frac{3}{11}+\frac{3}{19}+\frac{1}{19}\left(-2\right)x+\frac{2}{13}x<\frac{3}{13}
Multiply \frac{1}{19} and 3 to get \frac{3}{19}.
\frac{2}{11}x-\frac{3}{11}+\frac{3}{19}+\frac{-2}{19}x+\frac{2}{13}x<\frac{3}{13}
Multiply \frac{1}{19} and -2 to get \frac{-2}{19}.
\frac{2}{11}x-\frac{3}{11}+\frac{3}{19}-\frac{2}{19}x+\frac{2}{13}x<\frac{3}{13}
Fraction \frac{-2}{19} can be rewritten as -\frac{2}{19} by extracting the negative sign.
\frac{2}{11}x-\frac{57}{209}+\frac{33}{209}-\frac{2}{19}x+\frac{2}{13}x<\frac{3}{13}
Least common multiple of 11 and 19 is 209. Convert -\frac{3}{11} and \frac{3}{19} to fractions with denominator 209.
\frac{2}{11}x+\frac{-57+33}{209}-\frac{2}{19}x+\frac{2}{13}x<\frac{3}{13}
Since -\frac{57}{209} and \frac{33}{209} have the same denominator, add them by adding their numerators.
\frac{2}{11}x-\frac{24}{209}-\frac{2}{19}x+\frac{2}{13}x<\frac{3}{13}
Add -57 and 33 to get -24.
\frac{16}{209}x-\frac{24}{209}+\frac{2}{13}x<\frac{3}{13}
Combine \frac{2}{11}x and -\frac{2}{19}x to get \frac{16}{209}x.
\frac{626}{2717}x-\frac{24}{209}<\frac{3}{13}
Combine \frac{16}{209}x and \frac{2}{13}x to get \frac{626}{2717}x.
\frac{626}{2717}x<\frac{3}{13}+\frac{24}{209}
Add \frac{24}{209} to both sides.
\frac{626}{2717}x<\frac{627}{2717}+\frac{312}{2717}
Least common multiple of 13 and 209 is 2717. Convert \frac{3}{13} and \frac{24}{209} to fractions with denominator 2717.
\frac{626}{2717}x<\frac{627+312}{2717}
Since \frac{627}{2717} and \frac{312}{2717} have the same denominator, add them by adding their numerators.
\frac{626}{2717}x<\frac{939}{2717}
Add 627 and 312 to get 939.
x<\frac{939}{2717}\times \frac{2717}{626}
Multiply both sides by \frac{2717}{626}, the reciprocal of \frac{626}{2717}. Since \frac{626}{2717} is positive, the inequality direction remains the same.
x<\frac{939\times 2717}{2717\times 626}
Multiply \frac{939}{2717} times \frac{2717}{626} by multiplying numerator times numerator and denominator times denominator.
x<\frac{939}{626}
Cancel out 2717 in both numerator and denominator.
x<\frac{3}{2}
Reduce the fraction \frac{939}{626} to lowest terms by extracting and canceling out 313.
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Limits
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