3.
[tex]\frac{x-1}{2}+\frac{x-2}{3}+\frac{x-3}{4}>\frac{x-4}{5}+\frac{x-5}{6} <=>\frac{x+1}{2}+\frac{x+1}{3}+\frac{x+1}{4}>\frac{x+1}{5}+\frac{x+1}{6}+\frac{x+1}{x+1} <=> \frac{13}{12}(x+1)>(\frac{11}{30}+\frac{1}{x+1})(x+1) <=> \frac{13}{12}>\frac{11}{30}+\frac{1}{x+1} <=>\frac{1}{x+1}<\frac{43}{60} <=>43(x+1)>60 <=>x+1>\frac{60}{43} <=> x>\frac{17}{13}[/tex]