Question

What are the integer solutions to the inequality below?

Answer 1

3 < 3x - 3 ≤ 2x + 2

Adding -3 to each side gives

0 < 3x - 6 ≤ 2x - 1

The left inequality says

0 < 3x - 6   ⇒   3x > 6   ⇒   x > 2

while the right inequality says

3x - 6 ≤ 2x - 1   ⇒   x ≤ 5

Then the solutions belong to the interval 2 < x ≤ 5 and contains only the integers x = 3, x = 4, and x = 5.