Question

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

Answer 1

-3/2 ≤ x < 5

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

Answer 2

2x − 3 < x + 2
x − 3 < 2
x < 5

x + 2 ≤ 3x + 5
2 ≤ 2x + 5
-3 ≤ 2x
-3/2 ≤ x

Answer: -3/2 ≤ x < 5