Suppose that we are told that four numbers *a*,*b*,*c*,*d* lie between -5 and 5. Suppose also that the numbers are constrained so that

5 < *a*+*b *< 10 and -10 < *c*+*d *< -5

Given this information, what can you deduce about these inequalities?

?? < *a*+*b-c-d *< ??

?? < *a-c *< ??

?? < *a-c+d-b *< ??

?? < *abcd *< ??

*Did you know ... ?*

There are many useful general inequalities in mathematics, such as the AM-GM, Cauchy-Schwarz and Jensen's inequalities. These general inequalities are powerful tools which greatly simplify a wide variety of problems in mathematics, in applications from integration to probability via linear algebra.