Question

若不等式组2x+5a≤3(x+2),x-a/2≤x/3有解，且每一个解x均不在-1≤x≤4的范围内，求a的取值范围.

详细过程

Answer 1

解：由2x+5a≤3(x+2)，得
2x＋5a≤3x＋6
﹣x≤6－5a
x≥5a－6
由x-a/2≤x/3，得
2/3x≤a/2
x≤3/4a
∵不等式组2x+5a≤3(x+2),x-a/2≤x/3有解，且每一个解x均不在-1≤x≤4的范围内
5a－6＞4，3/4a＜﹣1
∴a＞2或a＜﹣4/3

Answer 2

2x+5a<=3(x+2)
2x+5a<=3x+6
x>=5a-6
x-a/2<=x/3
X<3a

5a-6<=x<=3a
又因为每个解在-1<=x<=4
所以5a-6>-1
3a<4
所以 1<a<4/3

Answer 3

2x+5a<=3(x+2)
2x+5a<=3x+6
x>=5a-6
x-a/2<=x/3
2x/3<=a/2
x<=3a/4
5a-6<=x<=3a/4
5a-6<=3a/4
20a-24<=3a
17a<=24
a<=24/17
5a-6>4
5a>10
a>2
3a/4<-1
3a<-4
a<-4/3
所以综合起来a<-4/3