On the straight line coordinate A (x + 3), point B (x-2) and C (2x + 5) points are located at the same distance, find what is x?

Let’s represent schematically all three numbers on a numeric one: A (x + 3); B (x – 2); and C (2x + 5), arranging them in ascending order.

B (x – 2) _______ A (x + 3) _______ C (2 * x + 5)

To find the distance between the points, subtract the smaller coordinate from the larger one, then we get:

1) AB = (x + 3) – (x – 2) = x + 3 – x + 2 = 5. But by the condition of problem 2) AB = AC = (2 * x + 5) – (x + 3) = 2 * x + 5 – x – 3 = x + 2.

Let us equate the resulting equation with the value from 1).

3) x + 2 = 5, whence x = 3.

Check: A (x + 3) = A (6); B (x – 2) = B (1); C (2 * x + 5) = C (11).

11 – 6 = 6 – 1 = 5.

Answer: x = 3.