When is the statement Below true for a≠0

Question

If a > -1 then 1/a < -1

When is the statement above true for a≠0

Answer 1

one counterexample disproves a proposition

if a > -1 then 1/a < -1 is false if a > 0 such as +2>-1 but +1/2 is not < -1

that leaves only the interval -1<a<0 such as a = -1/2 then 1/(-1/2) = -2<-1

if a>-2 then 1/a <-1 is true only if -1<a<0

it's true only if a is a negative proper fraction, with denominator greater than the numerator

such as -1/3, -3/4, - 15/16.

for "if a>-1 then 1/a <-1" is true only if a is in the interval open (-1,0)