I want explanation on how to prove this theorem: If b is greater than or equal to zero then absolute value of b is greater than a iff b is greater than a or b is less than negative a.
prove: If $b\geq 0$ then $|b|>a$ iff $b>a$ or $b<-a$.
0
$\begingroup$
algebra-precalculus
-
4if $b\ge 0$ then $|b|=b.$ – 2012-04-17
-
0It is not a theorem. It is just the definition. $|b| \geq a$ is equivalent to the $b \geq a$ or $b \leq -a$, because of the definition of $|b|$ which is $b$ for $b \geq 0$ and $-b$ for $b \leq 0$. – 2012-04-17