1. 6-5 Solving Absolute Value Equations
To learn how to solve Absolute Value Equations

2. What is Absolute Value?
The Absolute Value of a number is its distance from zero on a number line.
The symbol 𝑎 represents the absolute value of a.
Remember, since you are measuring distance the absolute value of a number will always be positive.

3. Absolute Value Equations
Consider the case 𝑥 =5.
This means the Distance between 0 and x is 5 units.
5 is five units from 0
-5 is also five units from 0
So 𝑥=5 𝑜𝑟 𝑥=−5
There are two solutions!

4. Absolute Value of a Number

5. So there are two cases… Case 1:
The value inside the absolute value symbol can be positive.
Case 2:
The value inside the absolute value symbol can be negative.

6. Ex 2: Solve an Absolute Value Equation

7. Ex 2: Solve an Absolute Value Equation

8. Ex 2B: Solve an Absolute Value Equation

9. Solving Absolute Value Equations
Isolate Absolute Value on one side of the equation.
Set up two equations one equals a positive distance one equals a negative distance.
Solve for the variables.
Check your answers.

10. Ex 3: No Solution
Because Absolut Value measures distance, we can never take an absolute value and get a negative value.
Because my absolute value expression equals a negative integer, there is no solution to this problem.

11. Checking Solutions…
It is important to check your solutions when solving absolute value equations.
Sometimes the answers may not be the correct solution to the original equation.

12. Ex 4: One Solution
So far it looks like my solutions are 4 and -1.

13. Ex 4: One Solution(Check)
So my solution is 4.