# Wearing a Smile or a Frown

- Author:
- Jaime Dianzon, Tim Brzezinski

## Is she happy or sad?

## OBJECTIVE: To learn how to solve absolute value equations

In a previous lesson, you learned about the concept of absolute value.

*Going the Distance:*https://www.geogebra.org/m/fyuu6q6n In this lesson, you'll learn how to solve absolute value equations.## STEPS IN SOLVING ABSOLUTE VALUE EQUATIONS:

Step 1: Isolate the absolute value expression.
Step 2: Check the number on the other side of the equation.
There are three cases:
Case 1: If the number is negative ( − ), there is no solution.
Case 2: If the number is zero ( 0 ), there is one solution. Remove the absolute value symbol from the absolute value expression, and solve for the unknown.
Case 3: If the number is positive, there are two solutions. Equate the algebraic expression inside the absolute value symbol to both the positive ( + ) and the negative ( − ) value of the number on the other side, and solve for the unknowns.
Step 3: Verify your answer/s.
Examples:
|2x − 4| = −10 ➽ No solution.
|2x − 4| = 0 ➽ 2x − 4 = 0
2x = 4
x = 2
|2x − 4| = 10 ➽ 2x − 4 = 10 or 2x − 4 = −10
2x = 14 2x = −6
x = 7 x = −3

## TRY IT YOURSELF ...

Solve the problems first on a separate sheet of paper and then type your answers in the boxes provided. Click the question mark to check your answers. If your answers are correct, a big "Correct!!!" sign will appear. Otherwise, you'll have to redo the problem.
Repeat as many times as needed to master the concept.

## In this lesson, you learned how to solve absolute value equations.

In future lessons, you'll also learn how to solve absolute value inequalities. Did you ENJOY today's lesson?