Hey there

Could you possibly help me with an induction which I couldn't understand, it was off an MGMAT CAT

The questions involves the expression

|x|xy + 9 > 0 // and we will later plaug in -1 for y

I can see how that is the same as

|x|xy > -9

And after plugging in -1, I can see how that becomes

|x|x (-1) > -9

And I can see how after diving by -1, which is a negative number the inequality becomes

|x|x < 9

What I can't get, is that the inequality, according to the solution was not reduced to

|x|x < 9 after division by -1

But instead, it was reduced to

x < 9

BOOOOM !! How did that happen ?

Since we are on this, I identified one of my weak points to be SPECIFICALLY inequalities/modulus in DS questions, how can I improve in this area ?

P.S I am not sure whether this post needs to go here or under Math problems, please let me know so I can make sure it sits in the right place