Inequality with absolute values |x+y|/(1+|x+y|) <= |x|/(1+|x|) +|y|/(1+|y|)
56315
Prove $\frac{|a+b|}{1+|a+b|}<\frac{|a|}{1+|a|}+\frac{|b|}{1+|b|}$.
66247
Proving inequality $\left( \frac {x} {y}\right) ^{x}\left( \frac {1-x} {1-y}\right) ^{1-x}\geqslant 1$
68986
Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$
135550
Inequality question­
91131
Question regarding an inequality
27570
Prove $(1-x)\ln(1-x)+(1+x)\ln(1+x)\leq 2x^2$ for $0<x<1$
38448
Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
14951
Other Idea to show an inequality $\dfrac{1}{\sqrt 1}+\dfrac{1}{\sqrt 2}+\dfrac{1}{\sqrt 3}+\cdots+\dfrac{1}{\sqrt n}\geq \sqrt n$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
61939
Induction of inequality involving AP
20816
Inequalities with assumptions and constraints
29935
If $a, b, c, d>0$ and $abcd=1$ prove that an inequality holds true
23979
Inequality involving sides of a triangle
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
12837
Inequality with condition $x^2+y^2+z^2=1$.
151148
How to solve simultaneous inequalities?
79040
Graph of $|x| + |y| = 1$