LESSON 3-6
COMPOUND INEQUALITIES
Objective: To solve and graph
inequalities containing “and” or
“or”.
Vocabulary

compound inequality – two inequalities joined by the
word and or the word or

solution for and inequalities – (Intersection) any
number that makes both inequalities true

solution for or inequalities – (Union) any number that
makes either inequality true
STEPS for AND problems
1.
Write the compound inequality as two inequalities
joined by and.
2.
Solve each inequality.
3.
Simplify and write the solutions as one statement.
4.
Graph the solution.
Translate the verbal phrase into an
inequality. Then graph the inequality.
a.
All real numbers that are greater than – 2
and less than 3.
Inequality:
–2<x<3
Graph:
b.
All real numbers that are less than 0 or greater than
or equal to 2.
Inequality:
Graph:
x < 0 or x ≥ 2
c.
All real numbers that are less than –1 or greater than
or equal to 4.
Inequality: x < –1 or x ≥ 4
d.
All real numbers that are greater than or equal
To –3 and less than 5.
Inequality: x ≥ –3 and x < 5
= –3 ≤ x < 5
Write and graph a real-world
inequality:
CAMERA CARS
A crane sits on top of a camera
car and faces toward the front.
The crane’s maximum height
and minimum height above the
ground are shown. Write and
graph a compound inequality
that describes the possible
heights of the crane.
Write and graph a real-world inequality:
SOLUTION
Let h represent the height (in feet) of the
crane. All possible heights are greater than
or equal to 4 feet and less than or equal to 18
feet. So, the inequality is 4 ≤ h ≤ 18.
You try…
Solve each inequality and graph the
solution.
1) -6 < 3x < 15
2) -3 < 2x-1 < 7
You try…
3) 7 < -3a + 1 < 13
Solution:
-4 < n < -2
You try…
4) The books were priced between $3.50
and $6.00, inclusive.

Solution: 3.50 < b < 6
To solve OR problems, solve
each inequality separately.
5) Solve –2x + 7 > 3 or 3x – 4 > 5.
Which inequalities describe the
following graph?
o
-3
1.
y > -3 or y < -1
2.
y > -3 and y < -1
3.
y ≤ -3 or y ≥ -1
4.
y ≥ -3 and y ≤ -1
Answer Now
-2
o
-1
Which is equivalent to
-3 < y < 5?
1.
y > -3 or y < 5
2.
y > -3 and y < 5
3.
y < -3 or y > 5
4.
y < -3 and y > 5
Answer Now
Which is equivalent to
x > -5 and x ≤ 1?
-5
2. -5
3. -5
4. -5
1.
<
>
>
<
x
x
x
x
≤
≥
≤
≥
1
1
1
1
Answer Now
Summary
• Re-write the compound inequality into two
problems and solve.
• For and problems, combine the solutions into
one statement.
• For or problems, solve each separately.
• Graph.
Exit Ticket
•Explain the difference
between “and” vs. “or”
compound inequalities.
•How do you solve a
compound inequality?
Homework:
•Page 349
•#’s 13-31 odd