The coordinates of points A and B are the roots of the equations | x-2 | = 7. Find the distance between points A and B.

Equations with modulus are solved as follows: if | x | = a, then x = a and x = -a.

| x – 2 | = 7. We get two equations: (a) x – 2 = 7 and (b) x – 2 = -7.

a) x – 2 = 7;

x = 7 + 2.

x = 9 – coordinate of point B.

b) x – 2 = -7;

x = -7 + 2.

x = -5 – coordinate of point A.

The distance between points A and B is equal to the modulus of the difference in the coordinates of these points:

AB = | 9 – (-5) | = | 14 | = 14.

Or AB = | -5 – 9 | = | -14 | = 14.

Answer: the distance between points A and B is equal to 14 unit segments.