**Inequalities Formulas**

1. Variables: x, y, z

Real numbers:

Determinants: D,

2. Inequalities, Interval Notations and Graphs

3. If a > b, than b < a.

4. If a > b , than a – b > 0 or b – a < 0.

5. If a > b , than a + c > b +c.

6. If a > b , then a – c > b – c .

7. If a > b and c < d , then a + c > b + d.

8. If a > b and c > d, than a – d > b – c.

9. If a > b and m > 0, than ma > mb.

10. If a > b and m > 0 , than.

11. If 0 < a < b and n > 0 , than an < bn.

12. If 0 < a < b, than <

13. ≤ ,

Where a > 0, b > 0; an equality is valid only if a = b.

14. a + ≥ 2, where a > 0; an equality takes place only at a = 1.

15. ≤ ,where

16. If ax + b > 0 and a > 0 , than x > .

17. If ax + b > 0 and a < 0, than x < .

18. + bx +c > 0

19.

20. If< a, than -a < x < a, where a > 0.

21. If > a, than x < -a and x > a where a > 0.

22. If x2 < a , than < , where a > 0.

23. If x2 > a , than > , where a > 0.

24. If

25. If