方程(2k-1)x+3k-2=0
(2k-1)x+3k-2=0
===> (2k-1)x=2-3k
===> 当2k-1≠0，即k≠1/2时：x=(2-3k)/(2k-1)
已知x不在区间[-1,1]内
则：
①x=(2-3k)/(2k-1)＞1
===> (2-3k)/(2k-1)-1＞0
===> [(2-3k)-(2k-1)]/(2k-1)＞0
===> (3-5k)/(2k-1)＞0
===> (5k-3)/(2k-1)＜0
(5k-3)*(2k-1)＜0
===> 1/2＜k＜3/5
②x=(2-3k)/(2k-1)＜-1
===> (2-3k)/(2k-1)+1＜0
===> [(2-3k)+(2k-1)]/(...全部
(2k-1)x+3k-2=0
===> (2k-1)x=2-3k
===> 当2k-1≠0，即k≠1/2时：x=(2-3k)/(2k-1)
已知x不在区间[-1,1]内
则：
①x=(2-3k)/(2k-1)＞1
===> (2-3k)/(2k-1)-1＞0
===> [(2-3k)-(2k-1)]/(2k-1)＞0
===> (3-5k)/(2k-1)＞0
===> (5k-3)/(2k-1)＜0
(5k-3)*(2k-1)＜0
===> 1/2＜k＜3/5
②x=(2-3k)/(2k-1)＜-1
===> (2-3k)/(2k-1)+1＜0
===> [(2-3k)+(2k-1)]/(2k-1)＜0
===> (1-k)/(2k-1)＜0
===> (k-1)/(2k-1)＞0
(k-1)*(2k-1)＞0
===> k＞1，或者k＜1/2
综上有：k∈(-∞,1/2)∪(1/2,3/5)∪(1,+∞)。
收起
