Solving absolute value Equations
Description/Explanation/Highlights
Video Description
In this video we learn to solve absolute value equations by splitting them into two cases and solving each equation (case) individually.
Steps and Key Points to Remember
To solve an absolute value equation, follow these steps:
- Begin by isolating the part of the equation that is inside the absolute value sign by performing the same Algebra operations to both sides of the equation to get rid of everything but the absolute value on one side of the equation.
- Next create two cases to represent positive and negative results.
- Write the first of these cases by writing the isolated equation exactly as it appears but without the absolute value sign.
- Write the second case by rewriting the absolute value side without the sign and the other side of the equation by making every term the opposite sign of the original.
- Solve each equation as a separate equation using Algebra rules to find the value of X.
- Check each solution for extraneous solutions by substituting it back into the original equation and solving to see if it is true.
- If solving the equation makes a true statement, that answer is valid.
- If solving the equation makes a false statement, that answer is not valid and must be eliminated.
- Be very careful with absolute value signs when checking.
Here are some key points to keep in mind when solving absolute value equations:
- After isolating the absolute value and making two cases, follow the Algebra rules to solve whatever type of equations are created. i.e. Every equation may not be linear.
- In creating the second case be sure to change EVERY sign on the side opposite the absolute value.
- All answers must be checked. Checking is not optional as extraneous solutions may be created in the process.
- After solving and checking there might be no solution, one solution, two solutions or more if a quadratic is
created for example.
Video Highlights
- 00:00 Introduction to absolute value equations
- 00:10 |X−6|+5=11 example with two valid solutions
- 01:10 Dividing the first example into two cases
- 02:30 Checking the first example to find that both solutions are valid
- 04:05 |X+10|=4X−5 example with one extraneous solution
- 05:40 Checking the second example to find the extraneous solution
- 07:15 |2X−1|+5=1 example with two extraneous solutions
- 08:40 Checking third example to find the extraneous solutions
- 10:40 Conclusion and website information