General Inequalities

Recall the inequality symbols <,>,

Note:

· Rather than having a solution to an inequality, we generally have a solution set.

· Two inequalities are said to be equivalent if the have the same solution set.

Properties of Inequalities

1. If a < b, then a + c < b + c and a – c < b – c.

2. (a) If a < b and c is positive, then ac < bc and a/c < b/c.

(b) If a < b and c is negative, then ac > bc and a/c > b/c.

3. The transitive property: If a < b and b < c, then a < c.

THEOREM Absolute Value and Inequalities

If a > 0, then

|u| < a if and only if –a < u < a

and

|u| > a if and only if u < - a or u > a