## Absolute value inequalities, Algebra

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In the earlier section we solved equations which contained absolute values.  In this section we desire to look at inequalities which contain absolute values.  We will have to examine two separate cases.

Inequalities Involving < and ≤

As we did with equations let's begin by looking at a fairly simple case.

p ≤ 4

This says that no matter what p is it ought to have a distance of no more than 4 from the origin. It means that p have to be somewhere in the range,

-4 ≤ p ≤ 4

We could have alike inequality with the < and obtain a similar result.

Generally we have the following formulas to use here,

If         |p| ≤ b, b = 0    then     - b ≤ p ≤ b

If         |p| < b, b =0     then     - b < p < b

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