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Cogito

Algebra 1 · Chapter 2 · Lesson 2

Practice Worksheet

Compound Inequalities

And narrows, or widens.

11 problems · about 22 minutes · A-REI.B.3, A-CED.A.1

NameDate

Figure — use these to answer the problems

Test a value against both parts and see whether it survives.
-10-9-8-7-6-5-4-3-2-1012345678910

4

A value to test4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. 4 < x < 10. Smallest whole number?

    Answer

  2. 2 < x < 6. Smallest whole number?

    Answer

  3. 2 < x < 6. Largest whole number?

    Answer

  4. 0 < x + 1 < 5. Largest whole number for x?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. x < 1 or x > 9. Does x = 5 work? 1 for yes, 0 for no.

    Answer

  2. x < 1 or x > 9. Does x = 10 work? 1 for yes, 0 for no.

    Answer

  3. Sort each compound inequality by whether anything satisfies it.

    Write each item under the heading it belongs to: x > 2 and x < 7 · x > 7 and x < 2 · x < 2 or x > 7

    Some numbers work

    Nothing works

Stretch Yourself

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

4 problems

  1. −3 < x < 3. How many whole numbers satisfy it?

    Answer

  2. Can an "or" inequality ever be empty? 1 for yes, 0 for no.

    Answer

  3. The Overlap

    x > 3 and x < 9. What is the smallest whole number that works?

    Answer

  4. The Empty Case

    x > 8 and x < 3. How many numbers satisfy it?

    Answer