3.6 solving compound inequalities. language goal students will be able to read and say compound...
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ALGEBRA 3.63.6 Solving Compound Inequalities
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LEARNING TARGETSLanguage Goal Students will be able to read and say
compound inequalities.
Math Goal Students will be able to solve and graph
compound inequalities.
Essential Question What are the differences between the
graphs of an inequality and a compound inequality?
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WARM-UP
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HOMEWORK CHECK
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HOMEWORK CHECK
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HOMEWORK CHECK
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HOMEWORK CHECK
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TAKE QUIZ 3.1 – 3.3 Good Luck!
You will do great!
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VOCABULARY Compound Inequality
Intersection
Union
When two simple inequalities are combined into one statement by the words AND or OR.
Example: x > 3 and x < -2
A compound inequality involving AND by using the idea of an overlapping region. Shows the numbers that are solutions of both inequalities.
A compound inequality involving OR by using the idea of combining regions. Shows the numbers that are solutions of either inequality.
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GRAPHING INEQUALITIES REVIEW
= open circle: Use for < or >
= closed circle: Use for or
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GRAPHING COMPOUND INEQUALITIES
Words Algebra Graph
All real numbers greater than 2 AND
less than 6
x > 2 AND x < 6
2 < x < 6
All real numbers greater than or
equal to 2 And less than or equal to 6
AND
All real numbers less than 2 OR greater than 6
x < 2 OR x > 6
All real numbers less than or equal to 2 OR greater
than or equal to 6
OR
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WHAT IS AN INTERSECTION?Draw each inequality separately then put them together.
0<𝑥 x<10
Together
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WHAT IS AN UNION?Draw each inequality separately then put them together.
𝑥<0 𝑥>10
Together
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PRACTICE GRAPHING Graph the following compound
inequalities.1. 2.
3. 4.
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WORD PROBLEM INEQUALITIES
Inclusive = means including the numbers specifically.
Therefore use the signs
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WORD PROBLEM INEQUALITIES A water analyses recommends that the
pH level of swimming pool water be between 7.2 and 7.6 inclusive. Write a compound inequality to show the pH levels that are within the recommended range. Graph the solution.
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WORD PROBLEM INEQUALITIES The free chlorine level in a pool should
be between 1.0 and 3.0 parts per million inclusive. Write a compound inequality to show the levels that are within this range. Graph the solution.
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WORD PROBLEM INEQUALITIES The pH of a popular shampoo is
between 6.0 and 6.5 inclusive. Write a compound inequality to show the pH levels of this shampoo. Graph the solution.
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SOLVING COMPOUND INEQUALITIES INVOLVING “AND” Solve each compound inequality and
graph the solutions.1. 2.
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SOLVING COMPOUND INEQUALITIES INVOLVING “AND” Solve each compound inequality and
graph the solutions.3. 4.
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SOLVING COMPOUND INEQUALITIES INVOLVING “OR”
Solve each compound inequality and graph the solution.
1.
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SOLVING COMPOUND INEQUALITIES INVOLVING “OR”
Solve each compound inequality and graph the solution.
2.
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SOLVING COMPOUND INEQUALITIES INVOLVING “OR”
Solve each compound inequality and graph the solution.
3.
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SOLVING COMPOUND INEQUALITIES INVOLVING “OR”
Solve each compound inequality and graph the solution.
4.
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SOLVING COMPOUND INEQUALITIES INVOLVING “AND”/“OR”
Solve each compound inequality and graph the solution.
1. 2.
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SOLVING COMPOUND INEQUALITIES INVOLVING “AND”/“OR”
Solve each compound inequality and graph the solution.
3. 4. 11
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WRITING A COMPOUND INEQUALITY FROM A GRAPH Write the compound inequality shown
by each graph.1.
2.
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LESSON QUIZ