|x−10| ≤ 20 modulus inequalities
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that is, we have:
| –2 | = | +2 | = 2
With this definition and picture in mind, let's look at some absolute value inequalities.
Solve | x | < 3, and graph its solution.
This is an inequality. Where the solution to an absolute-value equation is points (like in the graphic above), the solution to an absolute-value inequality (or "inequation") is going to be intervals.
In this inequality, they're asking me to find all the x-values that are less than three units away from zero in either direction, so the solution is going to be the set of all the points that are less than three units away from zero. First, I'll draw a number line:
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