Projection of a value from a range to another range?

Question

Mathematics

Unfortunately, I do not know mathematical terms well, so I can poorly formulate the question.
There is some value (coordinate). There are two coordinate systems.
Given:
Coordinate system I and coordinate system II.
1/n - scale of coordinate system II relative to coordinate system I (where n is an integer and greater than 0).
Coordinate systems are related at point 0.5, i.e. 0.5 on the second coordinate system is equal to 0.5 on the first coordinate system.
Thus, points 0 and 1 on the second coordinate system are respectively "0 - (1 / (2 * n))" and "1 - (1 / (2 * n))" on the first coordinate system.
Task: given the "x" coordinate on the second coordinate system, calculate the corresponding coordinate on the I coordinate system.
Illustration:

Perhaps the problem is solved corny, but I've been sitting with it for a long time ...