Let's solve each inequality and find the integer solutions.

1) $2 < x < 5$

• Integer solutions: $x = 3, 4$

2) $3 < x < 8$

• Integer solutions: $x = 4, 5, 6, 7$

3) $0 < x < 4$

• Integer solutions: $x = 1, 2, 3$

4) $-3 < x < 2$

• Integer solutions: $x = -2, -1, 0, 1$

5) $-7 < x < -4$

• Integer solutions: $x = -6, -5$

6) $-2 < x < 1$

• Integer solutions: $x = -1, 0$

7) $-4 \leq x \leq -1$

• Integer solutions: $x = -4, -3, -2, -1$

8) $-5 \leq x < -1$

• Integer solutions: $x = -5, -4, -3, -2$

9) $-3 < x \leq 1$

• Integer solutions: $x = -2, -1, 0, 1$

10) $2 > x > -1$

• Integer solutions: $x = 0, 1$

11) $-1 \geq x \geq -4$

• Integer solutions: $x = -1, -2, -3, -4$

12) $-2 > x \geq -7$

• Integer solutions: $x = -3, -4, -5, -6, -7$

Would you like more details on any of these solutions or have any questions?

Here are some follow-up questions to deepen understanding:

1. How would you solve inequalities that include fractions or decimals?
2. What is the difference between strict and non-strict inequalities?
3. How can inequalities be represented on a number line?
4. What happens if there are no integer solutions within the range of an inequality?
5. How do we handle inequalities when multiplying or dividing by negative numbers?

Tip: Always pay attention to whether an inequality is strict (using < or >) or non-strict (using ≤ or ≥) since it affects the inclusion of boundary values in the solution.