Solving and Graphing Compound Inequalities

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• Solving and Graphing Compound Inequalities

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• Inequalities Containing and
• To ride a roller coaster, you must be at least 52
  inches tall, and your height cannot exceed 72
  inches.
• If h represents the height of the rider, we can
  write two inequalities to represent this.
• At least 52 inches Cannot exceed 72 inches
• h 52 and h 72
• The inequalities h 52 and h 72 can be
  combined and written without using and as 52
  h 72
• Graph the inequality sandwich

Variable is isolated
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You try!
Inequalities Containing and

• Solve, graph, and write in interval notation.
• 1.) -2 lt x 3 lt 4
• 2.) -5 lt 3p 7 22

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• Inequalities Containing or
• SNAKES Most snakes live where the temperature
  ranges from 750 F to 900 F. Write an inequality
  to represent temperatures where snakes will not
  thrive.
• Let t temperature
• t lt 75 or t gt 90
• Graph the inequality torpedo

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You try!
Inequalities Containing or

• Solve, graph, and write in interval notation.
• 5n 1 lt -16 or -3n 1 lt 8
• The product of -5 and a number is greater than 35
  or at least 10.

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• OPEN ENDED 1 Write a compound inequality
  containing and for which the graph is the empty
  set.
• Sample answer x -4 and x 1
• OPEN ENDED 2 Create an example of a compound
  inequality containing or that has infinitely many
  solutions.
• Sample answer x 5 or x 1

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• Chemistry The acidity of the water in a swimming
  pool is considered normal if the average of three
  pH readings is between 7.2 and 7.8. The first
  two readings for the swimming pool are 7.4 and
  7.9. What possible values for the third reading
  p will make the average pH normal?

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The value for the third reading must be between
6.3 and 8.1, inclusive.
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• GEOMETRY The Triangle Inequality Theorem states
  that the sum of the measures of any two sides of
  a triangle is greater than the measure of the
  third side.
• a.) Write and solve three inequalities to express
  the relationships among the measures of the sides
  of the triangle shown above.
• b.) What are the possible lengths for the third
  side of the triangle?
• c.) Write a compound inequality for the possible
  values of x.