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

Solution:

It is given that inequality is

2x - 3 < x + 2 ≤ 3x + 5

Here

2x - 3 < x + 2

We can write it as

2x - x - 3 < 2

x - 3 < 2

x < 3 + 2

x < 5

x + 2 ≤ 3x + 5

We can write it as

2 ≤ 3x - x + 5

2 ≤ 2x + 5

2 - 5 ≤ 2x

-3 ≤ 2x

-3/2 ≤ x

Therefore, by solving the inequality we get -3/2 ≤ x < 5.

---

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

Summary:

By solving the inequality 2x - 3 < x + 2 ≤ 3x + 5 we get -3/2 ≤ x < 5.