6-4A Solving Compound Inequalities Involving

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6-4A Solving Compound Inequalities Involving
AND
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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What is a compound sentence in your English class?
This weekend I will go shopping and I will go to
a movie.
This weekend I will go shopping or I will go to a
movie.
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A compound inequality consists of two
inequalities connected by the word AND or the
word OR. Today we will work with the type
connected by the word AND. Compound
inequalities involving AND consist of two
inequalities. Both inequalities must be
satisfied to make the compound inequality true.
If you want to go to the movies with your friends
you must finish your homework and clean your room.
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Writing 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.
and
Compound inequalities with AND are generally
combined in a single inequality with the variable
in the middle.

O
0
4
Both inequalities must be satisfied to make the
compound inequality true. Therefore the solution
is the intersection (overlap) of the two rays.
The graph is a line segment! The number of
solutions are limited.
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Write a compound inequality that represents the
set of all real numbers greater than or equal to
2 and less than 8. Then graph the inequality.
and
Write the two inequalities.
Rewrite as a single inequality with the variable
in the middle.

O
2
8
Graph.
Note A compound inequality is usually written
in a way to reflect the order of numbers on a
number line.
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Example 1 Write a compound inequality that
represents the set of all real numbers greater
than or equal to -12 and less than -5. Then
graph the inequality.
Example 2 Write a compound inequality that
represents the set of all real numbers greater
than 2 and less than or equal to 3. Then graph
the inequality.
Example 3 Magic Mountains newest roller coaster
ride has weight restrictions of greater than or
equal to 50 pounds and less than 250 pounds.Write
a compound inequality to describe the weight
restriction and then graph the inequality.
Example 4 Write a compound inequality to
describe when water is liquid the temperature is
greater than 32 degrees F and less than 212
degrees F. Then graph the inequality.
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Example 1 Write a compound inequality that
represents the set of all real numbers greater
than or equal to -12 and less than -5. Then
graph the inequality.
and

O
-12
-5
Note A compound inequality is usually written
in a way to reflect the order of numbers on a
number line.
In a compound inequality involving AND, both
inequalities must be satisfied to make the
compound inequality true. Therefore the solution
is the intersection (overlap) of the two rays.
The graph is a line segment! The number of
solutions are limited.
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Example 2 Write a compound inequality that
represents the set of all real numbers greater
than 2 and less than or equal to 3. Then graph
the inequality.
and

O
2
3
You must label the endpoints!
You must label the endpoints!
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Example 3 Magic Mountains newest roller coaster
ride has weight restrictions of greater than or
equal to 50 pounds and less than 250 pounds.Write
a compound inequality to describe the weight
restriction and then graph the inequality.
and

O
50
250
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Example 4 Write a compound inequality to
describe when water is liquid the temperature is
greater than 32 degrees F and less than 212
degrees F. Then graph the inequality.
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Example 4 Write a compound inequality to
describe when water is liquid the temperature is
greater than 32 degrees F and less than 212
degrees F. Then graph the inequality.
and
O
O
32
212
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Write an inequality that describes the graph.

O
8
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1. Identify the endpoints.
2. Name the variable.
3. Write the inequality sign for each endpoint.
Note An inequality sign points toward the
smaller value thus both inequality signs point
in the same direction - to the left.
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Example 5 Write an inequality that describes the
graph.


2
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1. Identify the endpoints.
2. Name the variable.
3. Write the inequality sign for each endpoint.
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Solving Compound Inequalities with AND.
To solve compound inequalities with and,
isolate the variable. You must perform the
operation on all three expressions.

O
4
2
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Solve. Then graph the solution.
Example 6
Example 7
Example 8
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Example 6 Solve 5 lt 2x 3 lt 7. Then graph the
solution.

O
4
2
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Example 7 Solve 3 lt 1 2x lt 5. Then graph
the solution.
/
/
gt
gt
Reverse both inequality symbols.

O
3
1
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Example 8 Solve 2 lt 2x 1 lt 7. Then graph
the solution.
/
/
Reverse both inequality symbols.
gt
gt

O
3
3 2
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To solve a compound inequality involving AND,
isolate the variable (in the center). To perform
any operation on a compound inequality involving
AND, you must perform the operation on all
three expressions. The graph of the solutions to
a compound inequality involving AND is a line
segment.
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Homework
6-A5 Handout A5 (Study Guide and Intervention
Page 27).