SOLVING INEQUALITIES

Solve inequalities like an equation, but with small changes...

When solving inequalities, answers must be put into interval notation.

     -Interval Notation

          -Looks like a ordered pair, beginning with the smallest number and ending with the greatest number.

          -Put parenthesis when the number is not to be included in the solution, or a bracket to include the number.

          -Join solutions together with a union symbol, or a capital U between them.

               ex. If a solution is x>11, then the solution in interval notation begins with the smallest number (11) and

                    reaches to infinity.

When you multiply or divide by a negative number, flip the inequality sign.

     ex. -4x<4

            x>-1

If there are powers in the inequality, or a fraction with variables, you must set the inequality equal to zero and solve.

After solving, the solutions are called critical numbers, which must be set on a number line.

Finally, plug values that fit in each section of the number line and see which works to find the final solution to the inequality.

     ex. x^2-2x+1

          (x+1)(x-1)

          ------ -1 ------ 1 -------      Plug in values and see which sections are true, then write the intervals in interval notation.

You may find the following links helpful, interesting, wonderful, fantastic, delightful, pleasing, pleasurable, or all of the above!

Helpful Notes on Inequalities:

http://www.purplemath.com/modules/ineqsolv.htm

http://www.ronblond.com/M11/LinIne/index.html

Helpful Inequality Game: 

http://www.wikipedia.org/wiki/Inequality