Solving Absolute Value Inequalities
To solve an inequality means to find all values that make the inequality true. Absolute value inequalities are of the form f (x)< k, f (x)≤ k, f (x)> k, or f (x)≥ k. The graphical solution to an absolute value inequality is found using the same methods as for normal inequalities. The first method involves rewriting the inequality so that the
Example
Solve absolute value inequalities in two methods.
1. Solve
20 - 65x
< 8 by rewriting the inequality so that the
the inequality is zero.
2. Solve
3.5x + 4
> 10 by shading the solution region.
Before There may be differences in the results of calculations and graph plotting depending on the setting. Starting Return all settings to the default value and delete all data.
Set viewing window to
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— 8
GRAPH
2nd F CALC 5 * ➞ x = 10, y = 0
2nd F CALC 5 * ➞ x = 23.33333334
y= 0.00000006 ( Note)
Notes
20 - 65x < 8
➞20 - 65x - 8 < 0.
The intersections with the x- axis are (10, 0) and (23.3, 0) ( Note: The value of y in the
Since the graph is below the