Solving Absolute Value Equations What is absolute value

Solving Absolute Value Equations

What is absolute value? � 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 |5 x+7| = -8 is NO SOLUTION. � When you solve absolute value equations, you will almost always have 2 solutions.

How to solve Absolute Value Equations � 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

Examples � Example 1: Solve |5 x-6|+ 9 = 14 � Solution: |5 x-6|+ 9 = 14 � -9 -9 � |5 x-6| =5 � 5 x – 6 = 5 5 x – 6 = -5 � 5 x = 11 5 x = 1 � x = 11/5 x =1/5

� Example 2: Solve |45 x+8|= - 6 � Solution: NO SOLUTION !!!! (the absolute value, when isolated, is equal to a negative #) � |45 x+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!!!!!