SOSSS

a. Ta có: \begin{align*} &\frac{x+1987}{2002}+\frac{x+1988}{2003}>\frac{x+1989}{2004}+\frac{x+1990}{2005}\\ \iff & \frac{(x+1987)(2003\times 2004)+(x+1988)(2002\times 2004)}{2002\times 2003\times 2004}>\frac{(x+1989)(2002\times 2005)+(x+1990)(2003\times 2005)}{2004\times 2005\times 2002}\\ \iff & (x+1987)(2003\times 2004)+(x+1988)(2002\times 2004)>(x+1989)(2002\times 2005)+(x+1990)(2003\times 2005)\\ \iff & 2003\times 2004x+1987\times 2003\times 2004+2002\times 2004x+1988\times 2002\times 2004>2002\times 2005x+1989\times 2002\times 2005+2003\times 2005x+1990\times 2003\times 2005\\ \iff & 4002x>1989\times 2002\times 2005-1987\times 2003\times 2004-1988\times 2002\times 2004+1990\times 2003\times 2005\\ \iff & x>\frac{1989\times 2002\times 2005-1987\times 2003\times 2004-1988\times 2002\times 2004+1990\times 2003\times 2005}{4002}\\ \end{align*} Vậy đáp án là $\boxed{\frac{1989\times 2002\times 2005-1987\times 2003\times 2004-1988\times 2002\times 2004+1990\times 2003\times 2005}{4002}< x}$. b. Ta có: \begin{align*} &\frac{x-1}{99}+\frac{x-3}{97}+\frac{x-5}{95}<\frac{x-2}{98}+\frac{x-4}{96}+\frac{x-6}{94}\\ \iff & \frac{(x-1)(97\times 95\times 98)+(x-3)(99\times 95\times 98)+(x-5)(99\times 97\times 94)}{99\times 97\times 95\times 98} \\ &<\frac{(x-2)(97\times 95\times 94)+(x-4)(99\times 95\times 94)+(x-6)(99\times 97\times 98)}{98\times 96\times 94\times 99}\\ \iff & (x-1)(97\times 95\times 98)+(x-3)(99\times 95\times 98)+(x-5)(99\times 97\times 94)\\ &<(x-2)(97\times 95\times 94)+(x-4)(99\times 95\times 94)+(x-6)(99\times 97\times 98)\\ \iff & 97\times 95\times 98x-97\times 95\times 98+99\times 95\times 98x-99\times 95\times 294+99\times 97\times 94x-99\times 97\times 470\\ &<97\times 95\times 94x-97\times 95\times 188+(99\times 95\times 94)x-99\times 95\times 376+(99\times 97\times 98)x-99\times 97\times 588\\ \iff & 97\times 95\times 98x+99\times 95\times 98x+99\times 97\times 94x<97\times 95\times 94x+(99\times 95\times 94)x+(99\times 97\times 98)x\\ &+97\times 95\times 188+99\times