Given that x is an integer, what is the solution of |x-1|\leqslant 1 ​

Question

Given that x is an integer, what is the solution of
|x-1|
`\leqslant 1`
​

Answer 1

see explanation

Explanation:

Inequalities of the type | x | ≤ a always have solutions of the form

- a ≤ x ≤ a

Given

| x - 1 | ≤ 1 then

- 1 ≤ x - 1 ≤ 1 ( add 1 to each of the 3 intervals )

0 ≤ x ≤ 2

Since we require an integer solution then x = 0, 1, 2