Hi, I'm Steve Jones and I'm going to show you how to solve linear inequalities. Now there are one or two tricks about this that you don't get when you're solving linear equations. So let's just look at this carefully. Here, we've got four X minus two and it is less than eight. Just a warning, is that if we multiply or divide by a negative number we must change that for that or vice versa. Just a little one to remember because this is something that people do and they suddenly find they got the wrong answer and don't know why. Here we know we can actually deal with it as though it is an equation. But it isn't, it's an inequality. So four X minus two is eight, so what we can do is add the same to both sides. Because after all, if that is less than eight and I add two to there, and add two to there, it is this side is still going to be bigger than that. So if I add two here and I add two here, they're still going to be equal. This is the idea here we have six and here we have eight. Eight is bigger than six, but if I add to the eight I get ten, add two to the six I get eight, ten is still bigger than eight. It hasn't changed things. So what I'm now going to do is evaluate this. Four X minus two plus two will leave me with just four X here. I'll still have my less than and I've got eight plus two, that's ten. Well, that seems fairly straightforward. So what I must do now is divide by two, both sides, sorry not by two, by four don't I, divide by four. Because I've got four X. Okay. And I divide this side by four as well. Okay. So four X divided by four will just give me a plain X, I've still got less than and I've got ten divided by four, or two fours are eight, so that's two point five or two and a half, okay, so X is two and a half or two point five depending on how you're asked to express the result. So essentially what we're saying here, we've solved the equality, we know that the value of X is less than two and a half or two point five so it could be one, it could be zero, it cannot be two point five, X is not equal to two point five, it's less than. So it can't be equal to two point five and it can't be three or four or whatever after that. So here is X and there is two point five, so in fact, our number is everything - X is everything less than two point five. But not equal to two point five, so that is how we solve a linear inequality, and remember if I did come, if this was minus four X, then I'd have to be very careful because when I multiplied by a minus here, I have to change this around. Okay, good luck.
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