Prove: Use the triangle inequality to prove that for all $x, y, z, | x − z | ≤ | x − y | + | y − z |$
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
77576
Using the triangle inequalities to prove a bound in the complex plane
30044
Inequality with triangle sides
93599
General Proof for the triangle inequality
125817
show this inequality $(x+y)^3+(y+z)^3+(z+w)^3+(w+x)^3\ge 8(x^2y+y^2z+z^2w+w^2x)$
155341
Proving or disproving inequality $ \frac{xy}{z} + \frac{yz}{x} + \frac{zx}{y} \ge x + y + z $
25203
with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
66707
How to prove this inequality? $ | z-1 | \le | | z | -1 | + | z| \cdot | \arg z | $
137522
Hard inequality $ (xy+yz+zx)\left(\frac{1}{(x+y)^2}+\frac{1}{(y+z)^2}+\frac{1}{(z+x)^2}\right)\ge\frac{9}{4} $
156669
Trying to prove a simple (?) inequality
145783
How can I prove this inequality in a triangle: $\frac{1}{(b+c-a)} +\frac{1}{(c+a-b)} +\frac{1}{(a+b-c)} \gt \frac{1}{a} +\frac{1}{b} +\frac{1}{c}$?
86211
If $x+y+z \geq xyz$ Prove that $x^2 + y^2 + z^2 \geq xyz$.
81800
Prove inequality using Jensen's inequality
3820
Prove that $||x|-|y||\le |x-y|$
126632
Proving Inequalities with Absolute values
104217
Alternative triangle inequality proof