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SOLVING ABSOLUTE VALUE INEQUALITIES
Silvia V. asked • 08/30/16
A number is more than 9 units from 3
i would like to know how to make an inequality
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Arturo O. answered • 08/30/16
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You must account for both the number being more than 9 units smaller than 3 and being more than 9 units larger than 3. To do that, you set the absolute value of the difference between the number and 3 greater than 9.
Let x be the number
|x - 3| > 9
Now solve for x.
Suppose x - 3 is positive. Then
x - 3 > 9 ⇒ x > 12
Suppose x - 3 is negative. Then |x - 3| = -(x - 3) = 3 - x
Then
3 - x > 9 ⇒ x < -6
These are the 2 possibilities.
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