We are learning about inequalities. I originally assumed it would be the same as equations, except with a different sign. And so far, it has been - except for this.
Take the simple inequality: $-5m>25$ To solve it, we divide by $-5$ on both sides, as expected. $m>-5$.
But, I have been told that now we have to flip the inequality sign because we divided by a negative (and this also applies to multiplying negatives).
And this does work. Plug in any value less than $-5$ and it does turn out to be more than 25, but why?
Mathematically, why do we flip the sign here?