Question

1) x^2+5x< 0
2) x^2< 25
3) 2x^2-3x-5< 0

Answer 1

x^2 +5x<0

x * (x+5)<0

{x<0

{x+5>0

{x>0

{x+5<0

{x>0

{x<-5

x э (-5;0)

2. x^2<25

/x/<5

x<5, x>=0

x э [0,5)

x>-5, x<0

x э [0,5)

x э (-5,0)

3. 2x^2-3x-5<0

2x^2+2x-5x-5<0

2x×(x+1)-5(x+1)<0

(x+1)×(2x-5)<0

{x+1<0

{2x-5>0

{x+1>0

{2x-5<0

{x<-1

{x> 5/2

{x>-1

{x<5/2