Let 'x' be the length of the board cut.

Since it is acceptable for the length to differ from 2 m by at most 0.05 meters we the following absolute-value inequality:

|x - 2 | <= 0.5

Lets solve the inequality

1. If x >=2 then |x - 2| = x - 2

x - 2 <= 0.5

x < = 2.5

2. If x < 2 then |x - 2| = 2 - x

2 - x <= 0.5

x > = 1.5

The solution is 1.5 <= x < 2.5 and the range of acceptable lengths is 2.5 - 1.5 = 1