whenever you multiply or divide by a negative number..
you MUST flip the sign around, otherwise if you substitute a number into x.. or whatever inequality... it wont be true for both inequalities (the original AND the one that you multiplied a negative number with). ill give you an example...
THE RIGHT WAY
x > 1
(mutiply both sides by negative 1)
-x < -1
you can easily check, by subbing any number into x to prove it.
let's substitute x = 2 (since x is always greater than one.. from x>1)
therefore, 2 > 1.
now, sub it into the second inequality..
-2 < -1
which is also correct (since -1 is always greater than -2!)
good luck