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If the absolute value inequality is of the form where the absolute value of the difference between a variable (X) and some constant (a) is compared to another constant (b)

eg |X - a| compared with b, then

if the comparison is < or ≤, the compound inequality is a double inequality of the form c < X < d (or ≤),

and

if the comparison is > or ≥, the compound inequality is a disjoint inequality of the form X < c or X > d (or including the equals).

In both cases, c = b - a, d = b + a (>c)

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โˆ™ 2013-06-03 14:31:49
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Q: How can you tell what kind of compound inequality an absolute value inequality will represent?
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