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).
$m<-5$
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?
Best Answer
Surely you believe that we can add/subtract from inequalities without a problem. I show you why using this.
If you have that $x>y$, then subtract $y$ to get $x-y>0$ and subtract $x$ to get $-y>-x$. That is, multiplying by $-1$ flips the inequality.