Lesson video

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Hi everyone, it's Ms Jones here.

Today's lesson is all about solving inequalities graphically.

So we've seen how to solve simultaneous equations graphically but inequalities work slightly differently and we're going to be seeing how that works today.

Pause the video now, however, to make sure you have A, a pen and some paper, B, you've removed any distractions from around you and C, you've got a nice and quiet space to work if possible.

So do pause the video now to make sure you've got all of that ready so that we can begin.

Okay, let's make a start.

So the first part of today's lesson is the try this.

For each inequality, write five coordinates that satisfy it.

So we have y is less than two, we have x is greater than or equal to three and we have x add y is greater than five.

Can you come up with five coordinates for each of those three that satisfy it? So pause the video now to make sure you have done that.

So there were absolutely loads that you could have gotten but essentially, for the first one, we just needed to make sure that y coordinate is less than two, it cannot be two though.

For the second one, the x coordinate can be three and it can be anything larger than three.

So we could have had decimals, remember, there.

And for the last one, we needed two numbers in our coordinate that sum to makes a number greater than five.

So it couldn't be equal to five but we could have had, for example, 5.

5 by having 2.

5 and three.

We could've also included some negatives, like having negative one and seven, which sum to make six.

And there were loads that we could have used for that so well done if you got some of those.

We can plot inequalities on axes.

So we have here, for y is less than two, we had loads of coordinates that we could have created and we've plotted some of those here.

So y is less than two.

And we can see that there is quite a clear area where all of these points are.

And they are all under this line here.

The line of y equals two.

They are all underneath it because all of those points are less than two.

It's worth noting here that we have a dotted line and we'll talk a little bit more about that later.

For x is greater than or equal to three, again, if we were to just write down all of the coordinates we could think of and plot them on here, we would notice that they are all on this side of my line x equals three 'cause we want all of the x coordinates greater than three.

Thinking back to the previous graph that we saw on this one, what is the same and what is different about those graphs? Just pause the video now and have a little think.

So hopefully you noticed, as I pointed out in the previous one, we had a dotted line and this one is a full line.

That is because it depends on what we have with these symbols.

If it is just a less than or a greater than symbol, we have dotted lines because it's not including the line.

If we have a less than or equal to or a greater than or equal to symbol, we have a full line because we are including the points on that line.

You may also have noticed that they're in different directions.

Yes, it makes sense 'cause we've got x and y so we have, for y is less than two, we were looking at the line y equals two which is horizontal and for the x is greater than or equal to three, we were looking at x equals three which is vertical.

You might've noticed some other things as well so really well done if you did.

But that is the premise of those horizontal and vertical lines.

Let me have an inequality like this.

x add y is greater than five.

We don't just have a horizontal or a vertical line because if we were to rearrange that equation, or that inequality, sorry, to be more in the format of what we're used to with straight lines of y equals mx plus c, but obviously we don't have an equal sign here.

We would have y is greater than five subtract x or negative x add five.

And that is the line that we have plotted here.

We want all of the y values that are greater than the line y equals five subtract x.

So we've got everything above this line shaded.

And remember, this line is going to be a dotted line because it is just greater than, not greater than or equal to.

And that is how we plot inequalities and we show inequalities on axes.

Pause the video now to complete your independent task which I'll show now.

So the first question is asking you to find the inequalities that satisfy the coordinates below.

So if I have negative two, four, I'm looking for any inequalities that match with that coordinate, that that coordinate would satisfy.

So we could have just, for this one, had y is less than or equal to six.

And we can see that the y coordinate is four so that works.

For b, we could have had y is less than or equal to six because we've got a y coordinate less than or equal to six.

And we could have had y subtract x is less than one because negative seven subtract negative six is going to give me the answer of negative one, which is less than one so that works.

And the rest of the answers are here.

For question two you are asked, which of coordinates that were above, here, are satisfied by the following inequalities? So we have x add y is greater than or equal to one.

So 3.

5 add two is 5.

5, which is greater than or equal to one.

Three add negative two is one and that does work because it said it was greater than or equal to one and negative 2.

4 and 7.

4 is going get you five, which works for this one as well.

And the rest of the answers are there.

Really well done if you got some or most of those correct, great job.

How many different coordinates can you make using the numbers below? So we have negative five, zero, four and 12 that we can put into these boxes to create coordinates.

For each of the coordinates that you make, can you write three inequalities that it satisfies? I would love for you to try and think of unusual examples.

So it's quite easy to do x is greater than one, for example.

That works for any x value that's going to be greater than one.

But could you think of some more interesting examples like using both coordinates in them that's greater than something or maybe even using 2x subtract y is less than something that makes those coordinates that you've made work.

So pause the video now to have a go and experiment with those.

There were loads and loads of examples that you could have found and used for this one.

Here are just some examples that I have picked out.

So we could have used negative five here and something else here.

But for that negative five, we could have written, anything around the x value being less than negative 4.

5, for example, less than or equal to negative five, greater than or equal to negative five, less than 10.

Loads and loads of different things we could have used with just the x value.

If we'd have used zero and any of the other numbers here, we could have started talking about the y value.

So y is greater than or equal to zero, or less than or equal to zero, or it's greater than negative 0.

1 or it's less than one.

There were loads of different things we could have said for that.

And, again, as I asked you to try and experiment with having both of the values in there, that would've been brilliant.

So if we'd have used, for example, the coordinate four, twelve, you could have said that x add y is less than 17, or we could have said that y subtract x is greater than seven.

And as I said, there were an infinite number of things you could have written, absolutely loads of them.

So well done if you managed to write quite a few and extra well done if you managed to get some unusual ones, brilliant job.

Make sure you complete the quiz at the end of completing this lesson to test your understanding.

But you have done a brilliant job today when we were introducing inequalities and how to solve them graphically and we'll be doing more of this in the lessons to come.

Really well done, see you next time.