**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

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