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