Compound Inequalities

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Compound Inequalities
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Compound Inequalities

• Two inequalities that are joined by the word and
  or the word or

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AND

• This means that we are looking for where the
  solutions overlap.
• The answer must be a solution to BOTH
  inequalities.
• x gt 8 and x lt 12
• This would be all real numbers that are larger
  than 8 and 12 or less.

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AND
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Look at page 37 in your workbook.

• The diagram shows the number of boxes of oranges
  that an orange tree can produce in 1 year. An
  grower earns 9.50 for each box of oranges that
  he sells. How much can the grower expect to earn
  in 1 year from 1 tree? Explain your reasoning.

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• Whats another representation you could use to
  present your solution?
• All real numbers greater than or equal to -4 and
  less than 6.

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OR

• This means to take the two solution sets and
  combine them.
• The answer will be any number that is in EITHER
  set.
• x gt 11 or x lt 7

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OR
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Example 1

• Solve 3x 8 lt 7 and 2x 1 gt 5
• First, solve each equation
• 3x lt 15
• x lt 5
• 2x gt 4
• x gt 2
• Answer is x lt 5 and x gt 2

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Example 1 (cont)

• When your answer has AND you must write a
  repeated inequality
• Put the lower number on the left, the higher
  number in the right and the variable in the
  middle.
• Adjust the signs
• x lt 5 and x gt 2 would be
• 2 lt x lt 5

2 4 5
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Example 2

• Solve 3x 8 lt 11 or -2x 4 lt -16
• Solve each inequality
• 3x lt 3
• x lt 1
• -2x lt -20
• x gt 10
• x lt 1 or x gt 10

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Example 3

• 5 lt x 3 lt 12
• This means 5 lt x 3 and x 3 lt 12
• So, solve each equation.
• 2 lt x and x gt 9
• Combine
• 2 lt x lt 9
• Graph

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• An answer like x gt 5 and x lt 3 would become 3 lt x
  lt 5
• But, if I try to graph it, it will look like
  this.
• Where does it overlap? It has to overlap if it is
  and
• Since it does not overlap, the solution would be
  No Solution

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Try these

• 4x 3 lt -5 or 2x 7 lt 1
• -3 lt j 2 lt 7 (use and here)
• -5 lt 3x 1 lt 7

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Try theseanswers
-2 3

• 4x 3 lt -5 or 2x 7 lt 1
• -3 lt j 2 lt 7 (use and here)
• -5 lt 3x 1 lt 7

-5 5
-2 2