# Number Line Question

I am stomped on the following question

Which is greater judging from the number line if $\rm JL = KM.$

a) $\rm JK$

b) $\rm LM$

(Answer : Both are the same)

I would like to know how they concluded both are same ?

• $L-J=M-K\Rightarrow L-M=-K+J\Rightarrow M-L=K-J$. – David Mitra Aug 2 '12 at 14:57
• @DavidMitra . That makes sense. So on a number line $JL$ can be written as L-J right ? – MistyD Aug 2 '12 at 15:05
• Yes, $5-3 = 2$ as in: $-\stackrel{3}{|}-\stackrel{4}{|}-\stackrel{5}{|}-.$ – user2468 Aug 2 '12 at 15:07

We have $\rm JL = JK + KL$ and $\rm KM = KL + LM.$ (Exercise: why does these equalities hold?). Equate, simplify, and conclude.