2.1: Properties of Inequalities

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Here are some important properties of inequalities:

If \(a\), \(b\), and \(c\) are real numbers, then:

Transitive Property if \(a < b\) and \(b < c\) then \(a < c\)

Addition Property if \(a < b\) then \(a + c < b + c\)

Subtraction Property if \(a < b\) then \(a − c < b − c\)

Multiplication Property (Multiplying by a positive number) if \(a < b\) and \(c > 0\) then \(ac < bc\)

Multiplication Property (Multiplying by a negative number) if \(a < b\) and \(c < 0\) then \(ac > bc\)

Division Property (Dividing by a positive number) if \(a < b\) and \(c > 0\) then \(\dfrac{a}{c} < \dfrac{b}{c}\)

Division Property (Dividing by a negative number) if \(a < b\) and \(c < 0\) then \(\dfrac{a}{c} > \dfrac{b}{c}\)

There are no examples or homework in this section.

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