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Algebra I
6.4 – Solve Compound Inequalities
Learning Target: By the end of today’s lesson we should be able to successfully graph and solve compound inequalities.
COMPOUND INEQUALITY
A compound inequality that consists of two separate inequalities joined by ________ or __________.
And
The graph of a compound inequality with and is the
Or
The graph of a compound inequality with or is the
_________________of the graphs of the inequalities.
______________of the graphs of the inequalities.
x  3
x3
x2
x  2
 3  x and x  2
So,  3  x  2
x  2 or x  3
Write and graph compound inequalities.
1) Translate the verbal phrase into an inequality. Then graph the inequality.
a) All real numbers that are greater than or
c) All real numbers that are greater than –8
equal to – 2 and less than 2.
and less than or equal to –3.
b) All real numbers that are less than or equal
to 3 or greater than 6.
d) All real numbers that are greater than or
equal to –4 and less than 4.
Solve a compound inequality with and (Option #1 – Keep them together)
2) 15  3x  3  24
3) 15  7 x  1  50
Solve a compound inequality with and (Option #2 – Separate them)
4)  3  2x  1  11
5) 1  2x  3  19
Solve a compound inequality with or
6) 5x  6  9 or 2x  8  12
7) 9x  1  17 or 7 x  12  9
8) 3x  2  11 or 2x  8  16
Story Problem:
9) At an auction, the lowest bid for an autographed trading card is $20. The highest bid is $54. Write and graph a
compound inequality that describes the possible bids.