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?