Solve the inequality 2x - 3 < x + 2 ≤ 3x + 5. show your work.

-3/2 ≤ x < 5

Step-by-step explanation:

2x - 3 < x + 2 ≤ 3x + 5

2x - 3 < x + 2  

2x - x -3 < x - x + 2

x - 3 < 2  

x - 3 + 3 < 2 + 3

x < 5  

x + 2 ≤ 3x + 5  

x - x + 2 ≤ 3x - x + 5

2 ≤ 2x + 5  

2 - 5 ≤ 2x + 5 - 5

-3 ≤ 2x  

(1/2) -3 ≤ 2x (1/2)

-3/2 ≤ x  

-3/2 ≤ x < 5

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3