Question

Determine whether each statement is always, sometimes, or never true. explain your reasoning. A. |x|=|-x| _________ B. |x|=-|x| _______ C. |-x|=-|x| _______

Answer 1

A. $|-x|=|x| \Rightarrow |x|=|-x|$ always true

B. $|x|\geq0 \quad \forall_{x\in \mathbb{R}}$ so $|x|=-|x|$ is never true

C. same as B