Cogito
Algebra 1 · Chapter 2 · Lesson 3
Absolute Value Inequalities
Less than traps, greater than splits.
11 problems · about 23 minutes · A-REI.B.3
What this lesson teaches
The student solves absolute value inequalities and describes their solution sets.
- Less than traps the solutions into one interval around the centre.
- Greater than splits them into two intervals with a gap.
- An absolute value below a negative has no solutions at all.
Warm Up
Straightforward practice. Get the method working first.
4 problems|x| < 8. Largest whole number solution?
Answer 7
Why 7.
|x| < 3. Largest whole number solution?
Answer 2
Why Below 3.
|x| < 3. Smallest whole number solution?
Answer -2
Why Above −3.
|x| > 2. Smallest whole number above the gap?
Answer 3
Why Past 2.
Build It Up
The same ideas with more to keep track of.
3 problems|x − 4| < 2. What is the centre of the solution?
Answer 4
Why Distance is measured from 4.
|x − 4| < 2. Largest whole number solution?
Answer 5
Why Below 6.
Match each inequality to the shape of its solution.
Answer |x| < 5 → One interval around the centre; |x| > 5 → Two intervals with a gap; |x| < −1 → Nothing at all
Why A distance can never be under a negative.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problems|x| > 0. Which single number fails? Give it.
Answer 0
Why Its distance is not above zero.
|x| < −2. How many solutions?
Answer 0
Why Impossible.
Trapped: |x| < 6. What is the largest whole number solution?
Answer 5
Why 5.
Split: |x| > 6. What is the smallest whole number above the gap?
Answer 7
Why 7.