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6x+5+\frac{5}{3}x<5
Add \frac{5}{3}x to both sides.
\frac{23}{3}x+5<5
Combine 6x and \frac{5}{3}x to get \frac{23}{3}x.
\frac{23}{3}x<5-5
Subtract 5 from both sides.
\frac{23}{3}x<0
Subtract 5 from 5 to get 0.
x<0
Product of two numbers is <0 if one is >0 and the other is <0. Since \frac{23}{3}>0, x must be <0.