求不等式16<|x-10|<20的整数解

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求不等式16<|x-10|<20的整数解

求不等式16<|x-10|<20的整数解
求不等式16<|x-10|<20的整数解

求不等式16<|x-10|<20的整数解
16<|x-10|<20
-20

x>10时,16x<10时,16<10-x<20,解得-10综上,x=27,28,29,-9,-8,-7


先分解
16<|x-10|·····①
|x-10|<20·····②
由①得
x-10>16或x-10<-16
解得
x>26或x<-6
由②得
-20 -10所以原不等式组解集是
-10整数解为x=27,x=28,x=29,x=-9,x=-8,x=-7

case 1: x=10 false

case 2: x>10
16<|x-10|<20
1626solution for case 2: 26
case3: x<10
16<|x-10|<20
16<-(x-10)<20
6< -x<10
-10

全部展开

case 1: x=10 false

case 2: x>10
16<|x-10|<20
1626solution for case 2: 26
case3: x<10
16<|x-10|<20
16<-(x-10)<20
6< -x<10
-10solution for case 3: -10
solution of 16<|x-10|<20
case 1 or case 2 or case 3
ie 26

收起

|x-10|>16
|x-10|<20

x-10<-16或x-10>16
-20
x<-26或x>26
-20并交得-20 26整数解为
-21.-22.-23.-24.-25.27.28.29