Prove this statement (inequality): $|x-y| \leq|x-z|+|y-z|$
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
68986
Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
2504
Inequality $\left|\,x_1\,\right|+\left|\,x_2\,\right|+\cdots+\left|\,x_p\,\right|\leq\sqrt{p}\sqrt{x^2_1+x^2_2+\cdots+x^2_p}$
64096
Prove that $||z_1|-|z_2|| \leq |z_1-z_2|$.
118613
Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
103851
Show that $\frac{xy}{z} + \frac{xz}{y} + \frac{yz}{x} \geq x+y+z $ by considering homogeneity
23264
Inequality $ \vert \sqrt{a}-\sqrt{b} \vert \leq \sqrt{ \vert a -b \vert } $
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
143072
Proving $|\sin x - \sin y| < |x - y|$
18313
show this inequality with $xy+yz+zx=3$
119668
How prove this inequality: $\sum_{i,j=1}^{n}|x_{i}+x_{j}|\ge n\sum_{i=1}^{n}|x_{i}|$?
50273
How to prove $\lvert \lVert x \rVert - \lVert y \rVert \rvert \overset{\heartsuit}{\leq} \lVert x-y \rVert$?
156669
Trying to prove a simple (?) inequality
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
148451
Polynomial inequality proof