**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.