# Is -y>-x+4 equal to y>x-4?

Apr 12, 2015

No.
With an inequality, if you multiply both sides by a negative value the inequality is reversed
$- y > - x + 4$
is equivalent to
$y < x - 4$

One way to see this is to
add $\left(- y\right)$ to both sides:
$0 > \left(- x + 4\right) + y$
then subtract (-x+4) from both sides
$x - 4 < y$
which could be written
$y < x - 4$