Prove: $||x|-|y||\leq |x+y|$
3820
Prove that $||x|-|y||\le |x-y|$
109778
Proving $(x-c)|(p(x)-p(c))$
45370
Is it true that $|d(x, z) - d(y, z)| \leq d(x, y)$ and how do I prove it?
129331
Prove that $|x^p - y^p| \le p|x-y|(x^{p-1} + y^{p-1})$ provided that $1 \le p \lt \infty$ and $x, y \ge 0$
76863
How to show $ \sup \inf g(x,y) \leq \inf \sup g(x,y)$?
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
90343
Proving the inequality $|e^z-1|\leq e^{|z|}-1$
88328
Proof of $1+x\leq e^x$ for all x?
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
8207
Can I prove this inequality algebraically?
105316
Prove : $|x - y| \leqslant \epsilon$ $\forall \epsilon > 0$ iff $x = y$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
66247
Proving inequality $\left( \frac {x} {y}\right) ^{x}\left( \frac {1-x} {1-y}\right) ^{1-x}\geqslant 1$
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
2315
How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?
14952
Prove: $\frac{x}{\sqrt{y}}+\frac{y}{\sqrt{x}}\geq \sqrt{x}+\sqrt{y}$