Double inequality, Algebra

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The following is a double inequality.

                                                                  -9 <5 ≤ 6

In a double inequality we are saying that both of the inequalities have to be simultaneously true.  In this case 5 it is definitely greater than -9 and at the similar time is less than or equal to 6. Thus, this double inequality is a true inequality.

Conversely, 10 ≤ 5 < 20 is not a true inequality.  Whereas this is true that 5 is less than 20 (so the second inequality is true) this is not true that 5 is greater than or equal to 10 (thus the first inequality is not true). If even one of the inequalities into a double inequality is not true then the whole inequality is not true.  This point is more significant than you may realize at this point.  In a later section we will run across condition where several students try to combine two inequalities in a double inequality which simply can't be combined, so be careful.


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