We have the inequality:
-4 < (3x - 2)/5 ≤ 6
We multiply all the sides by 5:
-4*5 < 5*(3x - 2)/5 ≤ 6*5
-20 < 3x - 2 ≤ 30
Now, we add 2 to all the sides of the inequality:
-20 + 2 < 3x - 2 + 2 ≤ 30 + 2
-18 < 3x ≤ 32
Finally, we divide by 3:
-18/3 < 3x/3 ≤ 32/3
-6 < x < 32/3
Now, using interval notation:
x = (-6, 32/3]
This means that x takes all the values greater than -6 and less or equal to 32/3. Graphically, this is: