Projection of values from a range to another range?

Unfortunately, poor knowledge of mathematical terms, therefore, may be difficult to formulate a question.

There is a certain value (coordinate). There are two coordinate systems.

This:
The coordinate system I and coordinate system II.
1/n - scale coordinate system II relative to the coordinate system I (where n is an integer and greater than 0).
Coordinate systems are correlated at the point 0.5, i.e., 0.5 to the second coordinate system is equal to 0.5 in the first coordinate system.
Thus, the points 0 and 1 on the second coordinate system are respectively "0 - (1 / (2 * n)) and 1 - (1 / (2 * n))" in the first coordinate system.

Task: having a coordinate "x" in the second coordinate system, to calculate the corresponding coordinate in coordinate system I.

Illustration: Perhaps the problem is solved corny, but sit with her for a long time...
July 5th 19 at 00:07
July 5th 19 at 00:09
Solution
Make normal proportion
Suppose y is the desired value. x / y = 0 / (0 - (1/2n)) or x / y = 1 / (1 + (1/2n)) ? Depending on this, y will be different. Nor is any other case correct will not. Or am I wrong proportion are. - Keara.Harber commented on July 5th 19 at 00:12
: (x1-a1)/(b1-a1)=(x2-a2)/(b2-a2). a1 and b1, the border is shorter. a2 and b2 - more. Express x2 - Mandy62 commented on July 5th 19 at 00:15
x1 - coordinate into a smaller interval. x2 - more.
Further Express x1 or x2 is what you need.
n you have in the denominator? 1/(2n) or 1/2*n? - Mandy62 commented on July 5th 19 at 00:18
1/(2n), in the denominator... - Keara.Harber commented on July 5th 19 at 00:21
Trying to count. - Keara.Harber commented on July 5th 19 at 00:24
then x1=x2*(1+1/n)+1/(2n) - Mandy62 commented on July 5th 19 at 00:27
Wrong said. Now correct - Mandy62 commented on July 5th 19 at 00:30
For numbers from 0.5 to 1: x1=(x2*n+0.5)/(n+1) - Mandy62 commented on July 5th 19 at 00:33
For left side also. General answer: x1=(x2*n+0.5) / (n+1)

The proportion is: (x1-0,5) / (1-0,5)=(x2-0,5) / (1+1/(2n)-0,5) - Mandy62 commented on July 5th 19 at 00:36
It's magic. I'm a long time such tasks did not tried to solve, unsuccessfully and now solved. I was huge! - Keara.Harber commented on July 5th 19 at 00:39

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