2.6 Compound Inequalities Notes. Do not write on this sheet. Turn this sheet in when you are finished.
Please copy down the notes below and answer each of the questions. Write down any questions you still have
for Mrs. McLaughlin when you are finished.
There is a PowerPoint on Mrs. McLaughlin’s website that you can view to help you with this lesson if needed.
Tonight’s homework: page 101 all; page 102 # 5-7
Objectives: Solve compound inequalities with one variable.
Graph solution sets of compound inequalities with one variable.
Vocabulary:
compound inequality
intersection
union
The inequalities you have seen so far are simple inequalities. When two simple inequalities are combined into
one statement by the words AND or OR, the result is called a compound inequality.
Example #1 Graph x < 2 or x ≥ 4
a. First graph x < 2
b. Next graph x ≥ 4
c. Since this is a Union, unite the two graphs into one compound graph.
Example # 2 – Graph x < 4 and x ≥ 2
a. First graph x < 4.
b. Next Graph x ≥ 2.
c. Since “and” means intersection, find the intersection of both graphs for your final answer.
Intersections, or and statements are written as joint inequalities. The solution is 2  x  4 .
Check your understanding # 1.
Example # 3 Graph the compound inequality 6 < m < 8. (6 is less than m and m is less than 8)
a. First graph 6 < m (m >6).
b. Next graph m < 8.
c. Since the inequality is written as a joint inequality, it is an “and” statement. Find the intersection
between the two graphs.
Example # 4 Solve 3 < 2m – 1 < 9
Using Method 1:
a. Re-write the inequality as two separate inequalities.
3 < 2m-1 and 2m-1 < 9
b. Solve each inequality.
and
c.
Since this is an ‘and’ statement, find the intersection.
Example #5 Solve 3 2m  1 9
Using Method 2:
a.
Check your understanding # 2
Add 1 to all 3 parts of the inequality.
Next divide all 3 parts of the inequality by 2.
You are left with a joint compound inequality
Check your understanding # 3
Practice Problems:
Solve and graph the compound inequalities.
1. –5 < x + 1 < 2
2. 8 < 3x – 1 ≤ 11
3. 2x + 3 < 9 or 3x – 6 > 12
4. The pH level of a popular shampoo is between 6.0 and 6.5 inclusive. Write a compound inequality to
show the pH levels of this shampoo. Graph the solutions.
5. The free chlorine in a pool should be between 1.0 and 3.0 parts per million inclusive. Write a
compound inequality to show the levels that are within this range. Graph the solutions.
When you are finished with the above questions, check your work below. Re-work any questions that
you missed and you can begin your homework if there is extra time.
Answers to Questions:
Check your understanding:
1. B. This can also be written as -3 < y < -1
2. B
3. A
Practice problems:
1. -6 < x < 1
2. 3 < x ≤ 4
3. X < 3 or x > 6
4. 6.0 ≤ p ≤ 6.5
5. 1.0 ≤ c ≤ 3.0