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Let $x>y$ be two real numbers and $z \in R, z \neq 0$. Consider the following:
1.$\quad x+z>y+z$ and $x z>y z$
$2 \quad x+z>y-z$ and $x-z>y-z$
3.$\mathrm{xz}>$ yzand $\frac{\mathrm{x}}{\mathrm{z}}>\frac{\mathrm{y}}{\mathrm{z}}$
4.$x-z>y-z$ and $\frac{x}{z}>\frac{y}{z}$
Which of the above is/are correct?
Options:
1.$\quad x+z>y+z$ and $x z>y z$
$2 \quad x+z>y-z$ and $x-z>y-z$
3.$\mathrm{xz}>$ yzand $\frac{\mathrm{x}}{\mathrm{z}}>\frac{\mathrm{y}}{\mathrm{z}}$
4.$x-z>y-z$ and $\frac{x}{z}>\frac{y}{z}$
Which of the above is/are correct?
Solution:
1125 Upvotes
Verified Answer
The correct answer is:
$1,2,3$ and 4
All statements are correct.
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