|2t-3| = |2t| - |3t|

Question

( || = Absolute Value)

I squared both sides to get...

(4t^2)-12t+9 = t^2
Factored to...

(t-1)(t-3) = 0

My book says "Empty Set" for the answer.
What am I doing wrong?

Answer 1

Absolute values are always positive. For any t, |3t| will be larger than |2t| . So, the right side is always negative.
The absolute value of the left side is always positive.