algebra: write into absolute value?

Question

write into absolute value
10
(x is greater than or equal to 10 and x is less than or equal to 20)

Answer 1

10 ≤ x ≤ 20

This defines a range that is 10 wide (20 - 10) whose center is at 15 (average of 10 and 20).

Subtract 15 from "both sides":

10 - 15 ≤ x - 15 ≤ 20 - 15

-5 ≤ x - 15 ≤ 5

Then this is true if:

x - 15 ≤ 5 AND -5 ≤ x - 15

Or equivalently:

| x - 15 | ≤ 5