Question

Would I be correct in saying that |y| < -2 has no solution?

Answer 1

no
|y|=+-y
|y|<-2 => y<-2 & y>2

Answer 2

|anything| is 0 or positive, can anything less than -2 be 0 or positive?

Answer 3

No

Answer 4

Absolute value is basically defined as \[\Large \left| n \right| \ge 0\] ie the absolute value of any number is AT LEAST zero. Can't ever be smaller than 0.

Answer 5

So, yes you're correct.

Answer 6

OK, thanks guys.

Answer 7

yet another way to think about it
\[|a|<b\iff -b <a<b\]

Answer 8

^ that works too. And it'd tell you |y| < -2 ===> 2 < y < -2... ie y is greater than 2, but also less than -2 (which doesn't make sense)