# 🧭 Index - [[Absolute Value Rules]] - A collection of rules involving absolute values - [[Absolute Values]] - General definition of the absolute value - [[Proof of the Absolute Identity with the Square Root Rule]] - Proof that $|x|=\sqrt{ x^2 }$ - [[Proof of the Absolute Inequalities Rule]] - Proof for the inequalities $|x| \leq A$ or $|x| > A$ - [[Proof of the Absolute Value Power Rule]] - Proof for $|x^n|=|x|^n$ - [[Proof of the Absolute Value Product Rule]] - Proof that $|a||b| =|ab|$ - [[Proof of the Absolute Value Quotient Rule]] - Proof that $\frac{|a|}{|b|}= |\frac{a}{b}|$ - [[Proof of the Absolute Value Triangle Inequality]] - Proof that $|a+b| \leq |a| + |b|$