SOLUTION: If points A,B and C lie on a coordinate line and points A and B have coordinates of 15 and 7 respectively, then which of the possible coordinates for point C satisfy(ies) d(A,C)< d

If points A,B and C lie on a coordinate line and points A and B have
coordinates of 15 and 7 respectively, then which of the possible 
coordinates for point C satisfy(ies) d(A,C)< d(B,C)?

This is when C is closer to A than it is to B 

 |C - A| < {C - B|

|C - 15| < |C - 7|

The boundary equation is

|C - 15| = |C - 7|

This breaks into two equations:

C - 15 = C - 7 OR C - 15 = -(C - 7}
   -15 = -7    OR C - 15 = -C + 7
                      2C = 22
                       C = 11

So we set up a number line:

                         B                       A
                         |                       |
-------------------------------------o-------------------
-1  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17       

Then we test a point on either side of 11 in the original
inequality:

|C - 15| < |C - 7|

Say we pick test point less than 11, say 10

|10 - 15| < |10 - 7|
     |-5| < |3|
        5 < 3

That's false, so we DO NOT shade the line to the left of 11.

Now we pick test point greater than 11, say 12

|12 - 15| < |12 - 7|
     |-3| < |5|
        3 < 5

That's true, so we DO shade the line to the right of 11.

So the answer is C Î (11,¥).

                         B                       A
                         |                       |
-------------------------------------oCCCCCCCCCCCCCCCCCCCCC>
-1  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17

Edwin