How to prove $|x − y| ≤ |x| + |y|$, proof and reasoning
29679
Prove: $|x-y|\leq |x|+|y|$
14677
Proving the exponential inequality: $x^y+y^x\gt1$
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
121353
If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$
147892
Proving if $x<y$ then $\sqrt{x} < \sqrt{y}$
18016
Proof of the following inequality $ \frac{x - y}{\log x - \log y} > \sqrt{xy} $, $x>y$.
31299
Using the Fitch system, how do I prove $((p \implies q) \implies p)\implies p$?
91871
Proving quadratic inequalities?
96153
$ x^3<y^3 \iff x<y $ proof issue.
7775
Show that $|x-y|\leq |x|+|y|$.
46760
To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
42976
How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
64457
Prove:$|x-1|+|x-2|+|x-3|+\cdots+|x-n|\geq n-1$
157733
Are positive real numbers $x,y$ allowed to be taken out during this proof?
152311
Proving expression$\geq 2$, where variables are $x,y,z$
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$