For `x in R ,` find all possible values of (i)|x-3|-2` (ii) `4-|2x+3|`

Explanation

To solve the given problem, we will find the possible values for each part step by step.

### Part (i): Find all possible values of \(|x - 3| - 2\)

1. **Understanding the modulus function**: The expression \(|x - 3|\) represents the distance of \(x\) from 3 on the number line. The value of \(|x - 3|\) is always non-negative, meaning \(|x - 3| \geq 0\).

2. **Subtracting 2**: Since \(|x - 3| \geq 0\), we can write:
\[
...