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Cogito

Algebra 1 · Chapter 2 · Lesson 3

Practice Worksheet

Absolute Value Inequalities

Less than traps, greater than splits.

11 problems · about 23 minutes · A-REI.B.3

NameDate

Figure — use these to answer the problems

Test whether a value lies inside or outside the trap.

3

A value to test3

Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

|x| < 8. Largest whole number solution?
Answer
|x| < 3. Largest whole number solution?
Answer
|x| < 3. Smallest whole number solution?
Answer
|x| > 2. Smallest whole number above the gap?
Answer

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
|x − 4| < 2. Largest whole number solution?
Answer
7
Match each inequality to the shape of its solution.
Draw a line from each item on the left to its match on the right.
- |x| < 5
- |x| > 5
- |x| < −1
- One interval around the centre
- Two intervals with a gap
- Nothing at all

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
|x| < −2. How many solutions?
Answer
Trapped
|x| < 6. What is the largest whole number solution?
Answer
Split
|x| > 6. What is the smallest whole number above the gap?
Answer