Day 4: Solving Compound Inequalities
Warm Up
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Vocabulary
compound inequality
disjunction
conjunction
A compound sentence is a sentence that combines two simple sentences using the
word AND or the word OR. These sentences can be true or false depending on the
sentences themselves and which word joins the sentences together.
Exercise
Consider the following compound sentences. Tell whether they are true or false.
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Think and Write
 When is a sentence containing the word AND true? _______________________
________________________________________________________________
 When is a sentence containing the word OR true? ________________________
________________________________________________________________
Conjunctions
A statement that combines two inequalities using AND is called a conjunction.
The graph of a conjunction is the overlapping region, or intersection, between the
two individual inequalities.
Example
Two ways to write this conjunction are:
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Exercise A
𝑥<5
𝑥>2
𝑥 < 5 𝑎𝑛𝑑 𝑥 > 2
This conjunction is equivalent to: ____________________________________
𝑥 ≥ −4
𝑥 ≤ −1
𝑥 ≥ −4 𝑎𝑛𝑑 𝑥 ≤ −1
This conjunction is equivalent to: ____________________________________
𝑥<3
𝑥 ≥ −1
𝑥 < 3 𝑎𝑛𝑑 𝑥 ≥ −1
This conjunction is equivalent to: _____________________________________
Note: The symbol for the word “and” is
∧.
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Exercise B
____________ and ____________
f. Write a conjunction that is illustrated by the graph below in two ways:
_________________________________
________________________________
Compound sentence: ____________ and ____________
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Disjunctions
A statement that combines two inequalities using OR is called a disjunction.
The graph of a disjunction is the region formed when the graphs of the two individual
inequalities are combined. We shade the regions that are shaded at least once. This
combined region is called the union of the sets.
Example
Note: The symbol for the word “or” is ∨.
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Exercise A
𝑥>1
𝑥 < −3
𝑥 > 1 𝑜𝑟 𝑥 < −3
This disjunction is equivalent to: __________________________________________
𝑥>0
𝑥 ≤ −2
𝑥 > 0 𝑜𝑟 𝑥 ≤ −2
This disjunction is equivalent to: _________________________________________
𝑥 ≤ −2
𝑥≥3
𝑥 ≤ −2 𝑜𝑟 𝑥 ≥ 3
This disjunction is equivalent to: _________________________________________
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Exercise B
1) Graph the following compound sentence on the number line below.
2)
Is the following sentence true or false? Explain your reasoning.
3) . Write a compound inequality for the graph shown below.
_____________________________
4)
Name another inequality that is equivalent to the compound inequality you just graphed.
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Summary
Conjunctions
A conjunction is a compound sentence joined by AND. The solution set of a conjunction
is the set of values that make both inequalities true. This set is also called the
intersection of the two solution sets. On a graph, it is the area where the two individual
graphs overlap.
Disjunctions
A disjunction is a compound sentence joined by OR. The solution set of a disjunction is
the set of values that make either inequality true (or both). This set is also called the
union of the two solution sets. On a graph, it is the total area shaded by the two
individual graphs.
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Homework
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