1.7 Inequalities

Inequalities If a < b, then a+c < b+c If a < b and if c > 0, then ac < bc If a < b and if c < 0, then ac > bc Reverse direction of inequality symbol when multiplying or dividing by a negative number.

Interval Notation ( ) means number is not included in the solution setproblems with < > [ ] means number is included in solution set, problems with more than or equal to, or less than or equal toArrange from lowest to highest.

Quadratic Equations Solve the corresponding quadratic equation Identify the intervals determined by the solution Use a test value to determine which intervals determine which intervals form the solution set

Absolute Value Inequalities Case 1: When absolute value x = k, x = k or x = -kCase 2: When absolute value x < k, -k<x<kCase 3: When absolute value x > k, x < -k or x > k