Title: Solving Compound Inequalities Involving
1Compound Inequalities
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Understanding and. Understanding or.
2Conjunctions
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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3Definition 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
4- 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.
5- Solve Compound Inequalities with AND
Solve -2 lt x 2 ? 4. Then graph the solution.
6- Solve Compound Inequalities with AND
Solve -2 lt x 2 ? 4. Then graph the solution.
7- -1 lt x 3 lt 7
- -6 ? 3x ? 12
8Write a verbal sentence that describes the
inequality. Then graph the inequality.
1. y lt 0 or y gt 5
- y lt -3 or y gt 5
- y lt 7 or y gt 11
9- Solve Compound Inequalities with OR
Solve 3x 1 ? 4 or 2x 5 ? 7. Then graph
the solution.
10- Solve Compound Inequalities with OR
Solve x - 4 ? -8 or x 3 ? 5. Then graph
the solution.
11Solve the inequality. Then graph the solution.
- 7x ? 42 or x 5 ? 7
- x 7 ? 3 or 5x 5 ? 10