Question

已知m,n为实数，若不等式（2m-n)x+3m-4n<0的解集为x>4/9,求不等式(m-4n)x+2m-3n>0的解要有过程。谢谢

Answer 1

由不等式（2m-n）x+3m-4n＜0的解集为x＞4/9得
(2m-n)4/9=4n-3m且2m-n<0
即 8m-4n=36n-27m
35m=40n
7m=8n
令m = 8k n= 7k

(m-4n)x+2m-3n>0的解
x > (3n-2m)/ (m-4n) = (21k-16k)/ (8k-28k) = 5k /( -20k) = -1/4

x > -1/4

Answer 2

（2m-n)x+3m-4n<0
若2m-n<0，则n>2m
x>4n-3m/2m-n
由于x>4/9
则4n-3m/2m-n<=4/9
8n<=7m 与n>2m相矛盾
若2m-n>0,则n<2m
x<4n-3m/2m-n
4n-3m/2m-n>4/9
可得 7/8m<n<2m
m-4n<0,3n-2m>0
(m-4n)x+2m-3n>0
x<3n-2m/m-4n
不等式的解为：X<3n-2m/m-4n=-1-m+n/m-4n