How should I show that $|a+b|\geq||a|-|b||$?
3820
Prove that $||x|-|y||\le |x-y|$
133870
if $\alpha\leq\beta$ then there is $\gamma$ such as $\alpha+\gamma=\beta$
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
112969
Show that $ab + bc + ac \ge a\sqrt{bc} + b\sqrt{ac} + c\sqrt{ab}$
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
127296
prove that a|b and b|a iff a=+-b
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
110075
How to show the given equality
96217
If a and b are non-negative real numbers then demonstrate inequality
20863
how do I prove this inequallity?
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
85977
Show that if $\sqrt{a}+\sqrt{b}\neq 0$, then $\mathbb{Q}(\sqrt{a}+\sqrt{b}) = \mathbb{Q}(\sqrt{a},\sqrt{b}), \forall a,b\in\mathbb{Q}$
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
96327
Show that $a^x+b^x+c^x>(a+b+c)^x$ for all $a,b,c>0$ and $0<x<1$
81618
Prove $||a|-|b| | \leq |a-b|$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
118467
Prove that $a^2+ab+b^2\ge 0$