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Cogito

Algebra 1 · Chapter 1 · Lesson 6

Practice Worksheet

Absolute Value Equations

Two distances, so usually two answers.

11 problems · about 22 minutes · A-REI.B.3

NameDate

Figure — use these to answer the problems

Absolute value is distance from zero, measured either way.

5

A value5

Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

|x − 4| = 3. What is the larger solution?
Answer
|x| = 7. Positive solution?
Answer
|x| = 7. Negative solution?
Answer
|x − 3| = 5. What is the larger solution?
Answer

Build It Up

The same ideas with more to keep track of.

3 problems

|x − 3| = 5. What is the smaller solution?
Answer
|x| = 0. How many solutions?
Answer
|x + 1| = 4. What is the larger solution?
Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

|x| = −10. How many solutions?
Answer
9
Select every equation that has exactly two solutions.
- |x| = 2
- |x| = 0
- |x − 5| = 1
- |x| = −2
- Tick every box that applies.
The Positive Case
|x| = 9. What is the positive solution?
Answer
The Impossible One
|x| = −4. How many solutions?
Answer