I have to make certain assumptions about what you mean here by your
3 ≤ 4 + 3 x / 2 ≤ 2: 3 ≤ 4 + 3x/2 ≤ 2. Is that correct or not?
If correct, let's elim. the fractions by mult. all 3 terms of this inequality by 2:
2( 3 ≤ 4 + 3x/2 ≤ 2) => 6 ≤ 8 + 3x ≤ 4
Now subtract 8 from all three terms:
6-8 ≤ 8-8 + 3x/2 ≤ 2-8, or -2 ≤ 3x ≤ 4-8, or -2 ≤ 3x ≤ -4
Isolating x: -2/3 ≤ x ≤ -4/3
There's a basic problem here: -2/3 is not ≤ -4/3.
Please double check to ensure that you have copied down the original problem exactly as it was given.