Solution:

It is given that: | (3x – 4)/2 | ≤ 5/12

We can write the above equation as

| 3x/2 – 4/2 | ≤ 5/12

| 3x/2 – 2 | ≤ 5/12

Consider ‘r’ to be a positive real number and let ‘a’ be a fixed real number. Then, we can write:

|x – a| ≤ r ⟺ a – r ≤ x ≤ a + r

Here, a = 2 and r = 5/12

2 – 5/12 ≤ 3x/2 ≤ 2 + 5/12

(24-5)/12 ≤ 3x/2 ≤ (24+5)/12

19/12 ≤ 3x/2 ≤ 29/12

Upon multiplying the whole inequality both sides by 2 and then dividing by 3, we get the following inequality:

19/18 ≤ x ≤ 29/18

∴ x ∈ [19/18, 29/18]