Question 176364
1.{{{x>1}}}
All points to the right of x=1 satisfy that equation.
Now multiply the equation by (-1) and don't change the sign.
2.{{{-x>-1}}}
Now pick a point in the region that satisfies the original equation.
Let's pick x=3 and plug it into eq. 2,
2.{{{-x>-1}}}
{{{-3>-1}}}
Clearly -3 is not greater than -1. 
So you cannot satisfy both eq. 1 and eq. 2 because you have not changed the sign of the inequality. 
Not changing the sign leads to incorrect results, hence the reason the inequality sign needs to be changed.