Ch 6.4
Solving Compound Inequalities
Involving “AND”
Objective:
To solve and graph compound
inequalities involving “and”.
Definitions
Compound Inequality:
Two inequalities
connected by the words “and” or “or”
Inequality:
Two numbers or expressions that are not “strictly “
equal to each other.
They are separated by one of these symbols:
<
≤
>
≥
(less than) less than (greater than) greater than
or equal to
or equal to
Writing & Graphing an “and”
Compound Inequality
Write a compound inequality that describes all
the real numbers greater than -2 and less than 5.
x  2
x 5
and
2  x  5
-3
-2
-1
0
1
2
“In-between
statement”
3 4
5
6
Solve and graph the compound inequality.
4  x  3  7
4  x  3  7
4  x  3 and x  3  7
3
3
3  3
x 4
7  x
4  x  3  7
3  3  3
7  x  4
x  7 and x  4
7  x  4
-7
0
4
Solve and graph.
5  3x  4  7
4  4
4
9  3x  3
3
3
3
3  x  1
-3
0
1
Solve and graph.
4  6  x  8
6  6  6
10  x  2
10   x  2
1  1  1
10  x  2
2  x  10
-2
0
10
Solving Compound Inequality
Word Problems
1) What information do you have?
2) What are you trying to solve?
a. Determine the left side (of the inequality)
b. Determine the middle (of the inequality)
c. Determine the right side (of the inequality)
d. Determine which inequality sign to use
(can the left side be equal to the right side?)
A racquetball club charges a $20 membership
and $2 per hour. How many hours per month
can be played on a budget of $50 to $70?
Let x = # of hours
C = total cost
C = 20 + 2x
x 0 5 10
C 20 30 40
15
50
20
60
25
70
15  x  25
From 15 to 25 hours
30
80