Solving Absolute Value Equations

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.

What is absolute value?

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

How to solve Absolute Value Equations

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

Examples

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!!!!!