3≤ 4 + 3 x / 2 ≤ 2 solve the inequality. give the result in set notation and graph it

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.