Question

Points m,j,l and j lie on a line. Point j is between m and l , ml = 11 , kl=14 , and kj=9. What is mj?

Answer 1

We have points on a number lines, numbers basically, we'll call J, K, L and M.

We're interested in the lengths of line segments, which are the absolute differences of the numbers.

We have J between M and L.  Let's say L < J < M.

We have some leeway, let's just pin down L=0.  That's the origin of our number line.

Since ML=|M-L|=11 and L<M we conclude M=11.  Our inequality is

0 < J < 11.

Now we have KL=|K-L|=|K|=14 so K=14 or K=-14

|KJ|=9.

 Case 1: K=14, so 14-J=9 or 14-J=-9  so J=5 or J=23

 Case 2: K=-14 so -14-J=9 or -14-J=-9 so J=-23 or J=-5

We choose J=5 as the only one satisfying L < J < M.

L=0, J=5, M=11, K=14, MJ=|M-J|=|11-5|=6

Answer: MJ=6

Let's check ML=11, good, KL=14, good, KJ=9, good.