Properties o f Inequalities

1.7 – Linear Inequalities and Compound Inequalities Properties of Inequalities Addition and Subtraction Property of Inequality If a< b, then a + c < b + cor If a> b, then a+ c > b + c If a< b, then a - c < b - cor If a> b, then a - c > b - c Multiplication and Division Property of Inequality c is positive: If a< b, then a• c < b• cor If a> b, then a • c > b• c If a< b, then a/c< b/cor If a> b, then a/c> b/c c is negative: If a< b, then a• c>b• cor If a> b, then a • c<b• c If a< b, then a/c>b/cor If a> b, then a/c<b/c

1.7 – Linear Inequalities and Compound Inequalities Solving Inequalities Examples: -3 9 -2 10 -1 11

1.7 – Linear Inequalities and Compound Inequalities Solving Inequalities Examples: -1 -1 0 0 1 1 (1) Lost the variable (1) Lost the variable (2) False statement (2) True statement Solution: the null set Solution: All Reals

1.7 – Linear Inequalities and Compound Inequalities Properties of Inequalities Union and Intersection of Sets The Union of sets A and B represents the elements that are in either set. The Intersection of sets A and B represents the elements that are common to both sets. Examples: Determine the solution for each set operation. ) 5 -1 12 3 )

1.7 – Linear Inequalities and Compound Inequalities Compound Inequalities Example:

1.8 – Absolute Value Equations and Inequalities Absolute Value Equations Properties of Absolute Values Equations

1.8 – Absolute Value Equations and Inequalities Absolute Value Equations Examples:

1.8 – Absolute Value Equations and Inequalities Absolute Value Equations Example:

1.8 – Absolute Value Equations and Inequalities Absolute Value Inequalities Properties of Absolute Values Inequalities

Properties o f Inequalities