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Given this information, what can you deduce about these inequalities?
?? < a+ b- c - d < ??
Inner Equality
Age 16 to 18
ShortChallenge Level 
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 \quad\mbox{ and }\quad -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 < ??
?? < \frac{|a|+|c|}{2}-\sqrt{|ac|} < ??
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.
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.
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