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Prove that \[|xa|\left|\frac{1}{x}-\frac{1}{a}\right|=|x-a|.\]
Prove that $|ab|=|a|\,|b|$.
Prove that $|a|=0$ if and only if $a=0$.
Prove the triangle inequality.
Prove that $a\,b\leq|a|\,|b|$ for all real numbers $a$ and $b$.
Prove that $||a|-|b||\leq|a-b|$.
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Lesson Specific Problems
Prove that \[|xa|\left|\frac{1}{x}-\frac{1}{a}\right|=|x-a|.\]
Prove that $|ab|=|a|\,|b|$.
Prove that $|a|=0$ if and only if $a=0$.
Prove the triangle inequality.
Prove that $a\,b\leq|a|\,|b|$ for all real numbers $a$ and $b$.
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