New posts in Absolute Value

Area bounded by $2 \leq|x+3 y|+|x-y| \leq 4$

Minimum of $\left|1-\left(ab+bc+ca\right)\right|+\left|1-abc\right|$

Range of $f(z)=|1+z|+|1-z+z^2|$ when $ |z|=1$

Sides $\frac{|b - c|}{\sqrt{(b^2 + 1)(c^2 + 1)}}, \frac{|c - a|}{\sqrt{(c^2 + 1)(a^2 + 1)}}, \frac{|a - b|}{\sqrt{(a^2 + 1)(b^2 + 1)}}$ of a triangle.

Show that if $a,b \in \mathbb{R}^n$, then $|||a|| - ||b||| \leqslant ||a+b||$

How to solve double absolute value inequality?

Calculate the minimum value of $\left|\frac{a^2 - bc}{b - c}\right| + \left|\frac{b^2 - ca}{c - a}\right| + \left|\frac{c^2 - ab}{a - b}\right|$.

How to calculate $ \left| \sin x \right| $ derivative in a more elegant way?

Show that $|a|\leq \int_{-1}^{1}\,|ax+b|\,\text{d}x$

Is there a geometric analog of absolute value?