Cogito
Algebra 1 · Chapter 1 · Lesson 6
Absolute Value Equations
Two distances, so usually two answers.
11 problems · about 22 minutes · A-REI.B.3
What this lesson teaches
The student solves absolute value equations and recognises when none exist.
- Absolute value is distance from zero and is never negative.
- An absolute value equation usually splits into two cases.
- Equal to zero gives one solution; equal to a negative gives none.
Warm Up
Straightforward practice. Get the method working first.
4 problems|x − 4| = 3. What is the larger solution?
Answer 7
Why 7.
|x| = 7. Positive solution?
Answer 7
Why Seven from zero.
|x| = 7. Negative solution?
Answer -7
Why The other direction.
|x − 3| = 5. What is the larger solution?
Answer 8
Why x − 3 = 5.
Build It Up
The same ideas with more to keep track of.
3 problems|x − 3| = 5. What is the smaller solution?
Answer -2
Why x − 3 = −5.
|x| = 0. How many solutions?
Answer 1
Why Only zero itself.
|x + 1| = 4. What is the larger solution?
Answer 3
Why x + 1 = 4.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problems|x| = −10. How many solutions?
Answer 0
Why Impossible.
Select every equation that has exactly two solutions.
Answer |x| = 2; |x − 5| = 1
Why Zero gives one, a negative gives none.
The Positive Case: |x| = 9. What is the positive solution?
Answer 9
Why 9.
The Impossible One: |x| = −4. How many solutions?
Answer 0
Why None.