10.1: Properties of Inequalities
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.