Cogito
Algebra 1 · Chapter 2 · Lesson 2
Compound Inequalities
And narrows, or widens.
11 problems · about 22 minutes · A-REI.B.3, A-CED.A.1
What this lesson teaches
The student solves and graphs compound inequalities joined by and or or.
- An "and" inequality is satisfied only where both parts overlap.
- An "or" inequality is satisfied by anything either part covers.
- An "and" can be empty; an "or" never is.
Warm Up
Straightforward practice. Get the method working first.
4 problems4 < x < 10. Smallest whole number?
Answer 5
Why 5.
2 < x < 6. Smallest whole number?
Answer 3
Why Past 2.
2 < x < 6. Largest whole number?
Answer 5
Why Below 6.
0 < x + 1 < 5. Largest whole number for x?
Answer 3
Why Subtract 1 throughout.
Build It Up
The same ideas with more to keep track of.
3 problemsx < 1 or x > 9. Does x = 5 work? 1 for yes, 0 for no.
Answer 0
Why Neither part holds.
x < 1 or x > 9. Does x = 10 work? 1 for yes, 0 for no.
Answer 1
Why One part is enough.
Sort each compound inequality by whether anything satisfies it.
Answer Some numbers work: x > 2 and x < 7, x < 2 or x > 7 · Nothing works: x > 7 and x < 2
Why And needs an overlap; or never can be empty.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problems−3 < x < 3. How many whole numbers satisfy it?
Answer 5
Why −2 up to 2.
Can an "or" inequality ever be empty? 1 for yes, 0 for no.
Answer 0
Why Each part already has solutions.
The Overlap: x > 3 and x < 9. What is the smallest whole number that works?
Answer 4
Why 4.
The Empty Case: x > 8 and x < 3. How many numbers satisfy it?
Answer 0
Why None.