Triangle inequality for subtraction?
3820
Prove that $||x|-|y||\le |x-y|$
91131
Question regarding an inequality
68986
Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$
25203
with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
8207
Can I prove this inequality algebraically?
2504
Inequality $\left|\,x_1\,\right|+\left|\,x_2\,\right|+\cdots+\left|\,x_p\,\right|\leq\sqrt{p}\sqrt{x^2_1+x^2_2+\cdots+x^2_p}$
51120
Is this a valid proof for the reverse triangle inequality: Given $x,\,y\in\mathbb{R}^n$, $\|x-y\|\ge |\|x\| - \|y\||$.
77576
Using the triangle inequalities to prove a bound in the complex plane
71497
An inequality from Littlewood's Miscellany
111903
An inequality for sides of a triangle
52625
Prove inequality $\sqrt{\frac{2a}{b+a}} + \sqrt{\frac{2b}{c+b}} + \sqrt{\frac{2c}{a+c}} \leq 3$
136290
a mathematical problem on inequalities
47059
How to establish this inequality: $(1-a)(1-b)(1-c) \geq 8abc$ for $a+b+c=1$?
135120
Oppenheim's Inequality for triangles, American Mathematical Monthly problems
120390
An inequality involving 4 real or complex numbers
56101
Prove the inequality $\frac{a}{c+a-b}+\frac{b}{a+b-c}+\frac{c}{b+c-a}\ge{3}$
135550
Inequality question­