## More Advanced Inequalities

Any linear inequality of the formcan be solved just like a linear equation, by moving terms and changing signs for those terms that move to the other side of an equals sign:

It must be clear that when we multiple or divide by a negative number the inequality changes direction.

Inequalities can be much more complex, involving sums and products of various functions, some of which must be solved numerically. The simplest equations, which can be solved analytivally, involve products and quotients of linear terms.

Divide by -2 and factorise the numerator to obtain

Ifeverything is positive so

Ifthen left hand side is negative, sois not between 1 and 11 inclusive.

Ifthen every term factor is negative so whole left hand side is negative, sois greater than 1.

Henceor