Question

已知集合A=｛x|x＜-2或x≥3} B={x|ax+1＜0},若B含于A，求实数a的值的集合

Answer 1

A=x|x＜-2 or x≥3},  B={x|ax+1＜0}

ax+1<0

ax<-1

case 1: a<0

ax<-1

x> -1/a

B含于A

=>

-1/a ≥3

-1≤ 3a

a≥ -1/3

solution for case 1: -1/3≤a<0

case 2: a=0

B=Φ

=>B含于A

solution for case 2: a=0

case 3: a>0

ax<-1

x<-1/a

B含于A

=>

-1/a ≤-2

-1≤-2a

a≤ 1/2

solution for case 3: 0<a≤ 1/2

//

ie

B含于A

case 1 or case 2 or case 3

-1/3≤a<0  or a=0 or 0<a≤ 1/2

-1/3≤a≤1/2

Answer 2

A=x|x＜-2 or x≥3}, B={x|ax+1＜0}
ax+1<0
ax<-1
case 1: a<0
ax<-1
x> -1/a
B含于A
=>
-1/a ≥3
-1≤ 3a
a≥ -1/3
solution for case 1: -1/3≤a<0
case 2: a=0

B=Φ
=>B含于A
solution for case 2: a=0
case 3: a>0
ax<-1
x<-1/a
B含于A
=>
-1/a ≤-2
-1≤-2a
a≤ 1/2
solution for case 3: 0<a≤ 1/2
//
ie
B含于A

case 1 or case 2 or case 3
-1/3≤a<0 or a=0 or 0<a≤ 1/2
-1/3≤a≤1/2