2.  The absolute value of a number is its distance from 0.  Absolute value is always positive.  For example, from here to D.C. is approximately 40 miles. From D.C. to here, it is still 40 miles. (you wouldn’t say it’s negative 40 miles)  If you ever see the absolute value of something equal a negative number, you say NO SOLUTION.  For example |5x+7| = -8 is NO SOLUTION.  When you solve absolute value equations, you will almost always have 2 solutions.

3.  Step 1: Isolate the absolute value expression  Step 2: Make two separate equations that DO NOT have the absolute value symbol  One equation, positive, the other the negative version.  Step 3: Solve both equations  Step 4: Check to make sure they work

4.  Example 1: Solve |5x-6|+ 9 = 14  Solution: |5x-6|+ 9 = 14  -9 -9  |5x-6|= 5  5x – 6 = 5 5x – 6 = -5  5x = 11 5x = 1  x = 11/5 x =1/5

5.  Example 2: Solve |45x+8|= - 6  Solution: NO SOLUTION !!!! (the absolute value, when isolated, is equal to a negative #)  |45x+8|= - 6  Here are several examples on how to iso the absolute value.  And remember, once you have the absolute value expression by itself, you then set up 2 equations….one positive and one negative!!!!!