6.4
Solving Compound
Inequalities Involving “And ”
Goal
Solve and graph
compound inequalities
involving and.
Where can plants grow on a mountain?
The types of plant life on a mountain
depend on the elevation. At lower
elevations, trees can grow. At higher
elevations, there are flowering plants,
but no trees. At very high elevations,
there are no trees or flowering plants.
In Example 2 you will use inequalities
to describe such plant-life regions.
Key Words
• compound inequality
A compound inequality consists of two inequalities connected by the word and
or the word or. You will study the first type of compound inequality in this lesson.
You will study the second type in Lesson 6.5.
EXAMPLE
1
Write Compound Inequalities with And
Write a compound inequality that represents the set of all real numbers greater
than or equal to 0 and less than 4. Then graph the inequality.
Solution
Student Help
The set can be represented by two inequalities.
STUDY TIP
A number is a solution
of a compound
inequality with and if
the number is a
solution of both
inequalities.
0 ≤ x and x < 4
The two inequalities can then be combined in a single inequality.
0≤x<4
The compound inequality may be read in these two ways:
p x is greater than or equal to 0 and x is less than 4.
p x is greater than or equal to 0 and less than 4.
The graph of this compound inequality is shown below.
1
0
1
2
3
4
5
Write Compound Inequalities with And
Write a verbal sentence that describes the inequality.
1. 2 < y < 0
342
Chapter 6
Solving and Graphing Linear Inequalities
2. 7 ≤ t < 8
3. 4 ≤ n ≤ 11