## Basic College Mathematics (9th Edition)

We are given the statement $-|-4|\lt-|-7|$. We know that $|-4|=4$, because -4 is 4 spaces from 0 on the number line. Therefore, $-|-4|=-(4)=-4$. We know that $|-7|=7$, because -7 is 7 spaces from 0 on the number line. Therefore, $-|-7|=-(7)=-7$. Therefore, we can rewrite the statement as $-4\lt-7$. This statement is false, because -4 is to the right of -7 on the number line. So, -4 is greater than -7 in value.