Solving Double Inequalities

Video Transcript

"Hi, I'm Steve Jones and I'm going to show you how to solve a double inequality. Obviously what we're looking for is to find a range of X, where X sits, and at the moment X is sitting between these two numbers. But actually it's three X that is sitting between these two numbers so what we have to do first of all is make sure that we've got the solution for X and not three X. Well if I divide this by three, and if I divide this by three, and if I divide this by three, then we should get somewhere. So minus nine divided by three gives me minus three is equal to or less than, this is an equal to or less than. Right. So that means it can be equal to this and less than it. And three X divided by three is just X and twelve divided by three we know is four. Now, that is a fairly simple statement, all we have to do now is put it on to a kind of number line, here is the number line for X, so here is X. And we can start at zero if you want. Zero and one, two, three, four, five and so on. And here minus one, minus two, minus three, minus four, minus five. Now let's put this, so X, whatever values X can have, it's got to be less than four. So, this point is X equals four. That's X equals four there. But this is not included. All right, this is not included because X is less than four, so it can't be equal to four. So it's not equal to four. So that's why I put a red dot by it. Now, the other end is minus three, I'm going to put a green dot there and you can probably guess why, because we know that X can be equal to minus three, so it is included in that. But it can't be - what can it be? X is less than four, and it's also greater than or equal to minus three, so it can't be minus four, because that is less. So in fact, my number is here. It's this range, this is the range of numbers and it includes minus three, but it doesn't include X is four. So it includes X equals minus three, but it does not include X equals four. So here we've solved our double inequality, we have found the range of values from minus three including minus three to plus four, not including four, that is the range of values which are the solution of this double inequality. It's quite simple but be very careful."