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Inequality with z nonzero false statement

1000BeginnerAlgebraInequalities

Brazilian Mathematical Olympiad

If $x > 0$, $y > 0$, $x > y$ and $z \neq 0$, then the only incorrect option is: (A) $x + z > y + z$ (B) $x - z > y - z$ (C) $x z > y z$ (D) $\frac{x}{z^{2}} > \frac{y}{z^{2}}$ (E) $x z^{2} > y z^{2}$
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