Editing Elementary algebra (section)

==== Properties of inequality ====

The relations ''less than'' <math> < </math> and greater than <math> > </math> have the property of transitivity:<ref>Ron Larson, Robert Hostetler, ''Intermediate Algebra'', Publisher Cengage Learning, 2008, {{ISBN|0618753524}}, 9780618753529, 857 pages, [https://books.google.com/books?id=b3vqad8tbiAC&dq=algebra+inequality+properties&pg=PA96 page 96]</ref>
* If &nbsp; <math>a < b</math> &nbsp; and &nbsp; <math>b < c</math> &nbsp; then &nbsp; <math>a < c</math>;
* If &nbsp; <math>a < b</math> &nbsp; and &nbsp; <math>c < d</math> &nbsp; then &nbsp; <math>a + c < b + d</math>;<ref>{{cite web|url=https://math.stackexchange.com/q/1043755 |title=What is the following property of inequality called? |date=November 29, 2014 |work=[[Stack Exchange]] |access-date=4 May 2018}}</ref>
* If &nbsp; <math>a < b</math> &nbsp; and &nbsp; <math>c > 0</math> &nbsp; then &nbsp; <math>ac < bc</math>;
* If &nbsp; <math>a < b</math> &nbsp; and &nbsp; <math>c < 0</math> &nbsp; then &nbsp; <math>bc < ac</math>.
By reversing the inequation, <math> < </math> and <math> > </math> can be swapped,<ref>Chris Carter, ''Physics: Facts and Practice for A Level'', Publisher Oxford University Press, 2001, {{ISBN|019914768X}}, 9780199147687, 144 pages, [https://books.google.com/books?id=Ff9gxZPYafcC&q=turned+around&pg=PA50 page 50]</ref> for example:
* <math>a < b</math> is equivalent to <math>b > a</math>