Question from Wyatt:
I am not understanding Chapter 5 lesson 1 problems 26-31.
Wyatt
Answer from Dr. Callahan:
Given the figure
And that you are GIVEN
AB < BC < CD < DE
- #26 – AB < CD and BC < DE
This is true. Transitive - #27 – AB + BC < CD + DE
True. Addition Theorem of Inequality - #28 – AC < CE
Could be rewritten as AB + BC < CD + DE.
True. Addition - #29 – AD > DE
Could be written as AB + BC + CD > DE
False (Or we do not KNOW it is true). If AB = 1 inch, BC = 2 inch, CD = 3 inch, and DE = 3.1 inch this fits the given criteria but #29 will be false. So we are looking here for places where this is not ALWAYS true with what we are given. If not ALWAYS true, it is False. - #30 – BD > BC
Write as BC + CD > BC
True. Addition - #31 – AB < BD
AB < BC + CD
True – Addition.
