Help!!!!

2x - 3 < x + 2 ≤ 3x + 5    

Let's solve this in pieces

2x - 3 < x + 2      subtract x from both sides ....add 3 to both sides

x  < 5

And

 x + 2 ≤ 3x + 5       subtract x, 5 from both sides

-3 ≤ 2x         divide both sides by  2

-3/2 ≤ x

The solution comes from the intersection of these intervals........this is  [ -3/2, 5 )   or, expressed another way....-3/2 ≤ x < 5