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.
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![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.](/uploads/image/z/1635531-51-1.jpg?t=%E8%8B%A5%E4%B8%8D%E7%AD%89%E5%BC%8F%E7%BB%842x%2B5a%E2%89%A43%28x%2B2%29%2Cx-a%2F2%E2%89%A4x%2F3%E6%9C%89%E8%A7%A3%2C%E4%B8%94%E6%AF%8F%E4%B8%80%E4%B8%AA%E8%A7%A3x%E5%9D%87%E4%B8%8D%E5%9C%A8-1%E2%89%A4x%E2%89%A44%E7%9A%84%E8%8C%83%E5%9B%B4%E5%86%85%2C%E6%B1%82a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.)
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.
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.
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.
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
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
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