## Solving inequalities really do crop up in real life – it’s just a mathematical way of describing something…

This series of 3 minute math is designed as a quick reminder for some of the main topics. I hope they help to provide a focus and a way forward. If you need any more detail please search the site or contact me – always pleased to answer any questions!

All the very best with your studies.

### Where are inequalities used?

In the UK you need to be over the age of 17 to have a licence to drive a car. This could be written as an inequality:

In other words you have to be older than, or equal to, 17 to drive.

Inequalities can get a little more complicated and, at GCSE, tend to be given with two variables. As an example, lets say that you had £60 to spend and wanted to buy some T shirts (£3 each) and jeans (£17 each).

Let x be the number of T shirts and y be the number of jeans. The amount of money to be spent is less than or equal to £60. The equation would look like this:

### Transcript from the video:

“Welcome to 3 Minute Maths. This is all about solving inequalities. There are a couple different types of questions you’re going to get. Generally speaking, they tend to be fairly high level, A* types of questions, GCSE or equivalent.

You might get a question that’ll look something like this: . That’s a typical one mark or two mark question that you can treat in the same way as a linear equation. What we do is work out that the value of x is less than or equal to 12 by adding 3 to both sides – that will give us the ability to put x on one side all on its own.

– 3 + 3 is 0 so that’s going to mean we get , which is . That would be the answer to this question.

Now, the only type of ‘curveball’ they can throw is where they put in a fraction. So you get something which is like this: . That’s an A* type of question. Typically, this would be two marks, but we would treat it in much the same way as we would with any other linear-type equation.

To start, I’m going to multiply both sides by 3 because then I can get rid of the denominator and get 2x left on its own. It was but the 3’s cancel each other out. Then, on the other side of the inequality, I got 10 x 3, which is:

Well, means that to get the value of x itself, I divide both sides by 2. I got to get x on its own so I get .

And, those are really the only two types of questions that you’re going to get for solving inequalities. If you carry on watching the videos, we’ll have a look at more sophisticated versions of this. I hope you’ve found this useful and I’ll look forward to seeing you inside the next three minutes.”

Watch the video on YouTube Solving Inequalities as a Linear Equation

stephen barker says

closed includes open doesnt

stephen barker says

so if its -4 -3 -2 -1 0 1 2 3 4 open both ends from minus 3 to 3 for

solution if closed includes minus 4 is that right