Bitesize has changed! We're updating subjects as fast as we can. Visit our new site to find Bitesize guides and clips - and tell us what you think!
Print

Maths

Symbols, solving inequalities and graphs

Solving inequalities

An inequality such as 3x - 7 < 8 is similar to the equation 3x - 7 = 8. However, this time we are looking for numbers which if you multiply by 3, then subtract 7, you get an answer of less than 8.

Unlike 3x - 7 = 8, which has just one answer, there are lots of numbers for which this is true (in fact, an infinite number). So our answer is not a number, but a range of numbers.

We solve these inequalities just like simple equations: what you do to one side, you must do to the other.

Now have a look at this typical question:

Question

Solve the expression 3x - 7 < 8.

toggle answer

Answer
  • First, write down the inequality:
  • 3x - 7 < 8
  • Then add 7 to both sides, to cancel out the -7:
  • 3x < 15
  • Next, simplify the inequality by dividing both sides by the number in front of x - in this case 3.
  • x < 5

So the inequality in 3x - 7 < 8 is satisfied when x is less than 5. (Note that this does not include 5 itself.)

Sometimes the unknown appears on both sides, just as in simple equations.

Now look at this question.

Back to Algebra index

BBC © 2014 The BBC is not responsible for the content of external sites. Read more.

This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.