Question

How do you solve the compound inequality `h-10< -21` or `h+3<2`?

Answer 1

Solution: `h <-11 or (-oo , -11)`

Explanation:

`h-10<-21 or h < -21+10 or h < -11` or

`h+3<2 or h < 2-3 or h < -1`

The intersection of the two solutions is `h <-11`

Solution: `h <-11 or (-oo , -11)` [Ans]

Answer 2

`(-oo,-11)`

Explanation:

`"solve both inequalities"`

`h-10<-21larr" add 10 to both sides"`

`rArrh<-11`

`h+3<2larr" subtract 3 from both sides"`

`rArrh<-1`

`-11 < h < -1" only satisfies "h+3<2`

`"whereas "x < -11" satisfies both inequalities"`

`rArr(-oo,-11)" is the solution"`