Lesson video

Hello everyone is Mr. Millar here.

Welcome to the sixth lesson of the week on inequalities.

And in this lesson we're going to be continuing our work on forming and solving inequalities.

Okay.

So first of all, I hope that you're doing well and let's have a look at the try this example.

And in this lesson, we're going to be looking at setting up and solving inequalities in the context of word problems. Last lesson, we looked at it in the context of shapes, so here is word problems. So let's have a look.

What number could Yasmin be thinking of.

So she's saying, if I double my number and add three, I get less than, if I triple my number and subtract seven.

So, see if you can think of an example of a number that Yasmin could be thinking of that this works for and also that see if you can think of a number that would not work here, so at least one example of each.

Pause the video and have a go at this, try this.

Okay, great.

So I hopefully found an example of a number that did work and one that didn't and let's say for example, that you tried the number eight and what happens here.

So I double my number.

So double eight gives me 16 and then added three, well that would give a 19.

I compare that to, if I triple my number, so triple eight is 24 and then subtract seven is going to give me 17.

So does this work? Well, no it doesn't because at 19 is not less than 17, so eight couldn't be a number that she's thinking of.

But let's say you tried a 12, for example.

Well, this would work because if I doubled my number to get 24 and then added three, that would be 27.

Compare that to, if you triple my number.

So triple 12 is 36 and then subtract seven would give me 29.

So this does work, because 27 is less than 29.

So it works for eight, it works for a seven.

It doesn't sorry, it doesn't work for eight.

It doesn't work for seven.

It doesn't work for six, but it does work for some larger numbers.

So let's see if we can formalise this, by using some algebra.

So when you're ready let's move on to the connect slide.

Okay, so in the connect slide, we have exactly the same question as we had before, but this time we're going to form an equality and solve it.

So if you remember from last lesson, when we started off, we said, we'll let one of the lengths of the shape be equal to x.

So we'll do the same thing here and this is a common approach to take in maths.

So we're going to let the number, be equal to x.

We're going to call the number x.

So, let's find some expressions here.

So if I doubled my number and added three, so what is that going to be? Double my number and add three.

Well, double the number is going to be 2x, add three.

I get less than, so this is a less than, if I triple my number and subtract seven.

What's that going to be? Triple my number and subtract seven.

Well, it's going to be 3x triple my number subtract seven.

So there I have it.

I have formed an inequality in terms of x, where x is the number that I am starting off with.

Now, all I need to do is go ahead and solve this inequality.

So first of all, I notice I've got x's on both sides, so I'm going to subtract 2x from both sides here to get three is less than x minus seven, and then I'm going to seven to both sides.

So I'm going to have 10 less than x, or x is greater than 10.

So any number which is greater than 10, 11, 12, 13, that would work, but any number which is not, which is a 10 or less, is not going to work out with.

So again you can see that if I set up an inequality and solve it that can really really help me in these kinds of problems. In the independent task, you're going to have a look at similar problems. So when you're ready, I'd recommend you copy down this example.

So when you're ready, let's move on to the independent task.

Next, so here it is two questions, first of all.

The first one is a, show that question, so you need to set up an inequality to show that x is greater than four.

And then for question two, what I want you to do, is you first of all, need to, if you just read it together.

I think of a whole number, triple it, and then subtract two.

I call my answer eight, so we can let the whole number be x.

So when you triple x and subtract two, you need to think of an expression for the result of that and I want expressions or B and C as well.

And then what values could my starting number have, if A is less than B, B is greater than C, et cetera.

So pause the video now, to have a go at this independent task.

Okay.

So let's go through this very quickly.

So the first one, I think the number I'll call that x, I double it.

So that's going to be 2x and then add three.

My answer is greater than 11.

So I can say 2x plus three is greater than 11 and then I can just solve this.

So subtract three from both sides and then, there's not really enough space to do this.

So a subtracting three will get me 2x is greater than eight, and then divided by two gives me x is greater than four.

To question two, my expressions.

Well, A is going to be 3x minus two.

B is going to be x plus five that type all times by two or 2x plus 10, if I multiply that brackets and then the final one, I subtract x, I subtract it from 10 and then triple it, so I need a three outside of the bracket.

So that's going to be 30 minus 3x and now I can set up some inequalities.

So the first one A is less than B.

So I have that 3x minus two is less than 2x plus 10 and if I go ahead and solve this inequality, I would get the x is less than 12.

And B is greater than C, well, if I did this and solved it, I would have x is greater than four.

So if I wanted for the final one, x is less than B and B is greater than C.

I need to use both the inequalities, both the answers I've got in the previous case.

So x must be, more than four and less than 10.

So anywhere between those two values.

Great.

So, hope this makes sense.

Let's move on to the explore task when you are ready.

Okay.

So here's the explore task, let's have a look at, so Cala, Zaki and Yasmin are looking at the same positive number and they each saying a statement about that number.

Another student Xavier is saying, hang on something isn't quite right here.

So let's first of all, let's just say that this positive number that they're looking at, we'll call that x as we've been doing so far.

And then what I suggest you do is form an inequality, for each of these three students, and see if you can play around with these inequalities to find out why Xavier is thinking that there's something that's gone wrong here.

So pause video, try to create three different inequalities and see if you can find out what's gone wrong.

Okay, great.

So let's just work through each of these in turns.

So the first one, Cala is saying, if I double the number and add three, I get less than 23.

So I double the number.

So that's going to be at 2x, add three, I get less than 23.

And then if I solve this inequality, so subtract three from both sides, I get 2x is less than 20 and then divide by two I get x is less than 10.

So I know the number that they're thinking about, that they're looking at is less than 10.

What about Zaki? If I square the number I get more than 36.

So what can I write here? Well, if I square the number, so x squared, I get more than 36 and I'm told that it's a positive number so I don't need to worry about negative numbers here.

So I can just square roots and I can say that x is more than six.

So, so far, what do I have? I've got x is less than 10 and x is more than six.

So it seems to be okay, x is somewhere between a six and 10, but let's have a look at Yasmin statement.

So if I subtract triple the number from 42, I get less than six.

So I subtract triple the number from 42.

So 42 minus 3x, you can see I'm subtracting triple the number from 42 I get less than six.

And now we have to solve this inequality.

And what I do here, as I said before, when I have a negative coefficient of x, I like to move this.

So I have a positive one.

So I'm going to add 3x to both sides and I get 42 is less than six plus 3x and now I can subtract six, 36 is less than 3x.

And finally I can divide by three, so I have 12 is less than x or putting the x first, x is greater than 12.

So now that we have had a look and analysed all these statements, can you see what Xavier's point is? Well, on the one hand, Cala's statement suggests that x must be less than 10, but Yasmin statement suggests that x has to be greater than 12 and you can't have a number which is less than 10 and greater than 12.

That's obviously going to be impossible.

So that is, that is Xavier's point and that is what has gone wrong here.

So anyway, that has been the point of this lesson.

It's a really important lesson because we have to, it turns out that in math we have to sort of make statements from worded problems quite a lot.

So make sure that you have copied down this example as well and then there's a quiz for you to do in a worksheet as well, with more examples.

So thanks very much for watching and next time we're going to be looking at in more detail about the relationships between different inequalities.

Thanks very much for watching.

Have a good one and bye bye.