If we know that 0 < |x-3| < 2 then...
a) What does this tell us about the possible values of |x-1|?
b) What does this tell us about the possible values of |2x^2 - 8x + 6|?
For a) this is what I did:
If |x-3| < 2 then |x-1| < 4. Therefore any values greater than =3 but less than 5 will be true for |x-1| < 4
b) |2x^2 - 8x + 6| = |2x-2| |x-3| = 2|x-1| |x-3|.
If 2|x-1|<8 (as in above) then |x-1|<4. Put x=2 for 2|x-1|
2|x-3|<4, then |x-3|<2. Therefore, the solution is x=2. Correct?
I am sure for part a I am correct, but not for part b. If I did do wrong, what did I do wrong in part b?