How can you find the absolute value inequality equation when given the solution?

Question

Example:

Solutions: x > 7 or x < –5

Answer 1

abs(x - a) > b;

x - a > b or x - a < - b

x > a + b or x < a - b

a + b = 7

a - b = - 5

a = 1, b = 6

abs(x - 1) > 6

Answer 2

The absolute value function is symmetric around 0, so I'd look for an average.

Here we have 7 and -5, and the average is 1: 1 + 6 = 7, 1 - 6 = -5.

So |x - 1| > 6 when x > 7 or x < -5, as required.