3.6 Solving Compound Inequalities

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3.6 Solving Compound Inequalities

• Algebra 5.0
• Solve compound inequalities in one variable.
• Graph solution sets of compound inequalities in
  on variable.

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Vocabulary

• Compound inequality-when two simple inequalities
  are combined into one statement by words AND or
  OR.
• Intersection- this is the overlapping region of
  two numbers lines and shows the numbers that are
  solutions to both inequalities. (AND)
• Union- this is the combined regions and show the
  numbers that are solutions of either inequality.
  (OR)

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Intersection

• AND inequalities are segments

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Example-Intersections (AND)

• Solve using AND and the other by inverse
  operations. Graph solutions.

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Intersections (AND)

• Every solution of a compound inequality involving
  AND must be a solution of both parts of the
  compound inequality.
• If no numbers are solutions of both simple
  inequalities, then the compound inequality has no
  solutions.

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Practice

• Solve a using AND and b using inverse operations.
  Graph solutions.

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Union

• OR inequalities are opposite rays

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Example- Union (OR)

• Solve and graph solutions.
• OR inequalities typically have OR in them

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Example- Union (OR)

• The solutions of a compound inequality involving
  OR are not always two separate sets of numbers.
  This is rare, but not impossible.
• Some numbers may be solutions of both parts of
  the compound inequality.

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Practice

• Solve and graph solutions.

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Example-Writing Compound Inequalities from Graph

• Use the shaded region as the key.
• If the shaded portion is
• Between two values ? AND (2 ways to write them)
• Not between two values ? OR

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Practice

• Write the compound inequality shown by each
  graph. Write the AND two ways.

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Review

• Which compound inequality is an intersection and
  which is a union?
• What does the AND inequality and OR inequality
  look like?
• What are the two ways you can write an AND
  inequality solution?

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Review

• Solve and graph the inequalities.