Keystone Workshop
Unit 4 Day 2: Compound Inequalities
Warm-up
1) Simplify.
𝑥2
2𝑥 + 6
− 3𝑥 − 18
2) Write a system of equations to represent the following situation:
The admission fee at a small fair is$1.50 for children and $4.00 for adults. On a certain
day, 2200 people enter the fair and $5050 is collected. How many children and how
many adults attended?
Keystone Workshop
Unit 4 Day 2: Compound Inequalities
Warm-up
1) Simplify.
2𝑥 + 6
𝑥 2 − 3𝑥 − 18
2) Write a system of equations to represent the following situation:
The admission fee at a small fair is$1.50 for children and $4.00 for adults. On a certain
day, 2200 people enter the fair and $5050 is collected. How many children and how
many adults attended?
Keystone Workshop
Unit 4 Day 2: Compound Inequalities
Goal: Write or solve compound inequalities and/or graph their solution sets on a number
line (may include absolute value inequalities); Interpret solutions to problems in the
context of the problem situation (limit to linear inequalities).
I. Compound Inequalities

A _______________________________ is formed when two inequalities are joined
by the words ________ or __________.

A compound inequality with “and” can also be written as a single number sentence
with ______ inequality signs.
Ex:
𝑛 ≥ −3 and 𝑛 < 4 can also be written as __________________________________
𝑛 < 2 or 𝑛 ≥ 6

To find the solution to a compound inequality, solve each inequality separately.
Sometimes it helps to rewrite inequalities containing “and” as two separate inequalities.
Example 1:
II. Absolute Value Inequalities

Recall that expressions inside absolute value symbols can be positive or negative.
o Ex. Solve |5𝑝| = 15

For absolute value inequalities, you also need to split up the given inequality.
o The first inequality will be the same as the given without absolute value signs.
o For the second inequality, flip the inequality sign, and make the number after
it negative.
 Ex. Solve and graph |2𝑥 + 1| ≥ 9
Example 2:
HW: Pages 97-98 and Finish CRQs #1 and 2 on Pages 108 and 109.