Solving Compound Inequalities Involving

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Compound Inequalities
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Understanding and. Understanding or.
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Conjunctions
and
Mary had a little lamb and it
followed her to school one day.
or
Georgie Porgie ate the pie
or Georgie Porgie pulled out all the plums.
And implies that both must occur. Or implies
that one or the other will occur, but not
necessarily both.
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Definition A compound inequality consists of two
inequalities connected by the word and or the
word or.
Examples -7 lt x lt 10 x lt 8 or x gt 27 x lt
- 4 or x gt 4 12 ? x ? 30
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• The graph of a compound inequality with and is
  the intersection of the graphs of the
  inequalities.
• The graph of a compound inequality with or is the
  union of the graph of the inequalities.

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• Solve Compound Inequalities with AND

Solve -2 lt x 2 ? 4. Then graph the solution.
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• Solve Compound Inequalities with AND

Solve -2 lt x 2 ? 4. Then graph the solution.
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1. -1 lt x 3 lt 7

1. -6 ? 3x ? 12

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Write a verbal sentence that describes the
inequality. Then graph the inequality.
1. y lt 0 or y gt 5

1. y lt -3 or y gt 5

1. y lt 7 or y gt 11

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• Solve Compound Inequalities with OR

Solve 3x 1 ? 4 or 2x 5 ? 7. Then graph
the solution.
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• Solve Compound Inequalities with OR

Solve x - 4 ? -8 or x 3 ? 5. Then graph
the solution.
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Solve the inequality. Then graph the solution.

1. 7x ? 42 or x 5 ? 7

1. x 7 ? 3 or 5x 5 ? 10