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## 'Weekly Challenge 1: Inner Equality' printed from http://nrich.maths.org/

Inequalities are an important extension of algebra which are needed
more formally in C1 and beyond.

Note that some, but not all, algebraic manipulations still work
with equals signs 'replaced' by inequality signs -- you need to
take extra care when algebraically manipulating inequalities.

Addition or subtraction of a quantity is straightforward with
inequalities. For example, if we know that $5< a+b< 10$
then we know that $5-b< a< 10-b$. However, we need
to take more care with division and multiplication as minus signs
cause inequalities to reverse under these operations.

Direct algebra will not help you much in this problem. You will
have to make deductions such as 'if a is a very small positive
number than b must be very close to 5'.

Writing down such statements is difficult to do clearly, so
focus on the inequalities intuitively if need be.