Wetzel

Math 102

8.2 – Linear Inequalities and Absolute Value Inequalities

Inequality Symbols:             <     less than                                            less than or equal to

                                           >     greater than                                       greater than or equal to

Graphing on a number line:    1.)  Number line with significant numbers

                                             2.)  Open or Closed circle

                                             3.)  Arrow to the left or right

Interval Notation:                 1.)  Beginning Value, Ending Value

                                            2.)   and -

                                            3.)  ( ) or [ ]

Linear Inequality:  (One Variable)

                                To Solve:

                                                1.)  Solve the inequality as if it were an equation

                                                **2.) If you mult. or divide by a negative, “flip” the inequality sign

                Compound Inequalities ( “And” Inequalites)

                                *Solve for the variable in the middle

                “Or” Inequalities

                                *Solve both inequalites.  Solutions will be in one or the other.

                Examples:  Solve in Interval Notation and Graph.

                1.)                                               2.) 

                3.)    or 

Absolute Value Inequality: 

                                To Solve:

                                                1.)  Isolate the Abs. Value on the left side

                                                2.)  if < or ,

                                                                Rewrite as a compound inequality

                                                      If > or ,

                                                                Rewrite as an “Or” inequality

                                                3.)  Solve the remaining inequalities

                Example:  Solve.

                4.)                                                                       5.) 

                6.)                                                                       7.)