Question

e^x + xe^x > 0
the answer is ( -1, ∞)
what's the equation?
hint: the value of e^x is positive for all x.

Answer 1

it's simple

Answer 2

factor

e^x [ 1+x] >0

Answer 3

they have already told you that e^x>0 for all (they shouldn't have , it makes it too easy)

Answer 4

so the sign of the expression depends on the sign of (1+x)

Answer 5

(1+x)>0 , implies x>-1

Answer 6

=>e^x (x+1) >0
=> whatever x you will put e^x is never zero,it always come positive....only x+1 decides your sign
x+1>0
x>-1 hence (-1,infinity)

Answer 7

e^x (x+1)>0

(+ve number)(+ve number)>0 | or (-ve nymber)(-ve number)
i.e e^x >0 and x+1>0 |or e^x<0 and x+1<0
x belongs to (-&,+&) and x>-1 |or there is no x and x<-1
common x>-1 |or common nothing

finally x>-1