Absolute Values

Summary

• The absolute value of $x$ , denoted by $\left| x \right|$ is defined as

$$\left| x \right|=\{ \right.$$

• $\left| x \right|≥0$ for all real numbers $x$
• $\left| x \right|<a$ is the same as $-a<x<a$
• $\left| x \right|≤a$ is the same as $-a≤x≤a$
• Note,

$$\sqrt{x^2}=\left| x \right|$$