`#Rùa`
Đáp án+Giải thích các bước giải:
`g)(x+1987)/2002+(x+1988)/2003>(x+1989)/2004+(x+1990)/2005`
`⇔ ((x+1987)/2002-1)+((x+1988)/2003-1)>((x+1989)/2004-1)+((x+1990)/2005-1)`
`⇔ (x-15)/2002+(x-15)/2003>(x-15)/2004+(x-15)/2005`
`⇔ (x-15)/2002+(x-15)/2003-(x-15)/2004-(x-15)/2005>0`
`⇔ (x-15)(1/2002 +1/2003-1/2004-1/2005)>0`
Vì `1/2002>1/2004;1/2003>1/2005`
`⇒1/2002 +1/2003-1/2004-1/2005>0`
⇒ `x-15>0`
⇔ `x>15`
Vậy `S={x|x >15}`
`h)(x-1987)/2002+(x-1988)/2003>(x-1989)/2004+(x-1990)/2005`
`⇔ (1+(x-1987)/2002)+(1+(x-1988)/2003)>(1+(x-1989)/2004)+(1+(x-1990)/2005)`
`⇔ (x+15)/2002+(x+15)/2003>(x+15)/2004+(x+15)/2005>0`
`⇔ (x+15)/2002+(x+15)/2003-(x+15)/2004-(x+15)/2005>0`
`⇔ (x+15)(1/2002+1/2003-1/2004-1/2005)>0`
Vì `1/2002>1/2004;1/2003>1/2005`
`⇒1/2002 +1/2003-1/2004-1/2005>0`
⇒ `x+15>0`
⇔ `x> -15`
Vậy `S={x|x > -15}`
`k)(x+1)/99+(x+3)/97+(x+5)/95<(x+2)/98+(x+4)/96+(x+6)/94`
`⇔ (1+(x+1)/99)+(1+(x+3)/97+(1+(x+5)/95)<(1+(x+2)/98)+(1+(x+4)/96)+(1+(x+6)/94)`
`⇔ (x+100)/99+(x+100)/97+(x+100)/95<(x+100)/98+(x+100)/96+(x+100)/94`
`⇔ (x+100)/99+(x+100)/97+(x+100)/95-(x+100)/98-(x+100)/96-(x+100)/94<0`
`⇔ (x+100)(1/99+1/97+1/95-1/98-1/96-1/94)<0`
Vì `1/99<1/98;1/97<1/96;1/95<1/94`
⇒ `1/99+1/97+1/95-1/98-1/96-1/94<0`
⇒ `x+100>0`
⇒ `x> -100`
Vậy `S={x|x > -100}`
