Solve inequality by factoring help

[DeanBH]

x^2 + 8x + 15 > 0 solve inequality

(X+5)(X+3)>0


x+5>0 x>-5
X+3>0 x>-3

Why is the equality for X+5>0 x<-5 ? as the answers give?

 

[Physicsissuef]

Because you have two possible solutions for (x+5)(x+3)>0

the first one:

x+5>0 ; x>-5

x+3>0 ; x>-3

$$(-5, +\propto) \cap (-3, +\propto) = (-3, +\propto)$$

and the second

x+5<0 ; x<-5

x+3<0 ; x<-3

$$(-\propto, -5) \cap (-\propto, -3) = (-\propto, -5)$$

The final solution:

$$(-\propto, -5) \cup (-3, +\propto)$$

Anyway, this way is much more time-consuming... So you shouldn't use it in future.. There is much easier way...

 

[DeanBH]

Because you have two possible solutions for (x+5)(x+3)>0

the first one:

x+5>0 ; x>-5

x+3>0 ; x>-3

$$(-5, +\propto) \cap (-3, +\propto) = (-3, +\propto)$$

and the second

x+5<0 ; x<-5

x+3<0 ; x<-3

$$(-\propto, -5) \cap (-\propto, -3) = (-\propto, -5)$$

The final solution:

$$(-\propto, -5) \cup (-3, +\propto)$$

Anyway, this way is much more time-consuming... So you shouldn't use it in future.. There is much easier way...

you could have just said

"because if X > -5 then the first bracket will become negative and then (x+5)(x+3) wouldn't be > 0."


but ok. =P

btw : i just realized why