$|x| - |y| \leq |x-y|?$
3820
Prove that $||x|-|y||\le |x-y|$
155136
$x\in \{\{\{x\}\}\}$ or not?
20816
Inequalities with assumptions and constraints
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
50273
How to prove $\lvert \lVert x \rVert - \lVert y \rVert \rvert \overset{\heartsuit}{\leq} \lVert x-y \rVert$?
77130
How to prove this inequality $\left|x\sin{\frac{1}{x}}-y\sin{\frac{1}{y}}\right|<2\sqrt{|x-y|}$?
91877
Let $|x|\leq1, |y|\leq 1$. Show that$0 \leq x^{2}+y^{2} -2x^{2} y^{2}+2xy \sqrt{1-x^{2}} \sqrt{1-y^{2}} \leq 1$
153823
$|\text{rank}A-\text{rank}B|\leq \text{rank}(A+B)$
80009
Prove that $| |a|-|b| | \le |a-b|$
133870
if $\alpha\leq\beta$ then there is $\gamma$ such as $\alpha+\gamma=\beta$
93157
If $A \subseteq B$, does $\mbox{dist}(x,\partial A) \le \mbox{dist}(x, \partial B)$ hold for all $x \in A$
8207
Can I prove this inequality algebraically?
77026
Proof with inequalities
31295
$x+y\sqrt{2}$ infimum ($x,y\in \mathbb{Z}$)
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
51347
Prove that $|a|\leq \max\{|b|,|c|\}$ if $b\leq a \leq c$
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$