Chapter Fourteen — Quadratic Equations and Inequalities
The Humongous Book of Algebra Problems
321
Substitute test values from the intervals (such as x = –3, x = –1, , and x = 1)
into the inequality to identify the solution.
The solution to the inequality is x < –2 or .
Note: Problems 14.42–14.43 refer to the inequality 4x
3
+ 5x
2
– 6x < 0.
14.43 Graph the solution to the inequality.
According to Problem 14.42, the solution to the inequality consists of two
intervals: x < –2 and . Plot them both on the same number line, as
illustrated by Figure 14-8.
Figure 14-8: The solution to the inequality 4x
3
+ 5x
2
– 6x < 0.
It’s easier
to plug the test
values into the
factored version of
the inequality:
x(x + 2)(4x – 3) < 0
instead of
4x
3
+ 5x
2
– 6x < 0.
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