In math, an inequality is something in the form a > b or a < b. By solving them, you find what is called their solution set - the values for which the inequality is true.

Linear inequalities

These can be solved in two simple ways -
  • Testing with values.
  • Using algebra.
Imagine the inequality t + 2 > 6t + 7. The first method of solving this would simply involve guessing at numbers for t until we hit on one that worked. This is slow, and solving it algebraically is much quicker.

When performing algebra on an inequality, it can be treated identically to an equation, except that when multiplying or dividing by a negative number, the inequality sign is reversed. Follow this -

t + 2 > 6t + 7
-5t > 5
(gathering together like terms)
t < -1 (dividing both sides by -5, note the inequality sign is reversed!)


Quadratic inequalities

Because quadratic inequalities have a number of different solutions, you are seeking a solution set greater than 1. For this reason, it is best to plot them on a graph (simply replace the inequality sign with an equals sign and plot it), then read the solution set off. The solution set is between the roots of the quadratic equation, but you will usually need to refer to a graph to decide on where exactly between them it lies.