Lesson video

Hi everyone, this lesson is about representing inequalities on number lines.

Here is an inequality.

X is greater or equal to three.

This means that X is a range of numbers greater than or equal to three.

Here is a list of numbers.

Which of these numbers is satisfied by the inequality X is greater than or equal to three? Well 10 would, three would be, 234 would be, but one would not.

Here is the inequality X is greater or equal to three represented on a number line.

I need to draw a fully shaded dot above the number three and then I draw an arrow pointing in the same direction as the inequality.

This number line represents the inequality X is greater or equal to three.

Here is a different inequality.

X is greater than three.

I represent this inequality on a number line using an empty dot.

This shows that the number three is not included in the inequality.

I finish of by drawing an arrow in the direction of the inequality.

Here is the inequality X is greater than zero.

Does the inequality match what is represented on the number line? Yes, they are matching.

Here's another example.

X is less than or equal to zero.

Is that represented on the number line? In this case, yes they are matching.

Last example, X is less than two.

Matching? Not in this case.

The arrow points in the same direction as the inequality but I have used a fully shaded dot and it should've been an empty dot.

They are not matching.

Here are some questions for you to try.

Pause the video and return to check your answers.

Here's the solutions to question number one.

Remember, if you have a greater than or less than symbol, represent it with an empty dot and if you have a symbol which is greater than and equal to or less than and equal to, then use a fully shaded dot.

Let's try questions two and three now.

Pause the video and come back to check your answers.

Here's the solutions to questions two and three.

Now, number lines don't have to go up in ones.

Here's an example where it's going up in 50s and I have the, oh, I have the inequality which is X is greater or equal to 50.

So, here the arrow represents the fact that this includes all the numbers going into infinity, okay.

There we go, just a different type of number line for you to look at.

Here's some new notation for you to have a look at.

This inequality means the range of numbers between zero and three so X is between zero and three.

So how do I represent the inequality X is between zero and three on a number line? Here's by number line.

I draw a fully shaded dot above zero, another fully shaded dot above three and then I join them with a line.

The number line represents X is between zero and three.

What's different about this example compared to the last one? If you look, the inequality signs are different.

Instead of using a fully shaded dot, we're going to use empty dots above the numbers zero and three on our number line.

I draw a line between those two dots and this represents the inequality X is between zero and three, not including zero and not including three.

So what's different with this example? This inequality, we have two signs which are different.

That means on my number line, above the zero I would draw a fully shaded dot, and above the three it would be an empty dot.

Remember to join those two dots together with a line.

This is the inequality X is between zero and three, not including three represented on a number line.

Does this inequality match what is represented on the number line? Yep, they do, they are matching.

Notice we've got fully shaded dots above minus two and two and then a line drawn between them.

So here's a number line, here's an inequality.

The number line reads X is between minus one and three but not including three.

Does that match the inequality? Yes it does, yep, yep, yep, yep.

Think about this example.

Are they matching? In this case, they're not so they are not matching.

Here are some examples for you to try.

Pause the video and return to look at your answers.

Here's the solutions to question number four.

Question four A, the inequality is X is between negative three and one, inclusive.

That is mathematical terminology for saying that negative three and one are included in our inequality.

In question four B, the inequality is X is between negative three and one, exclusive.

That means that it excludes the integer negative three and the integer one.

Using precise mathematical terminology can help us to understand the question better.

Here are some examples for you to try.

Pause the video and return to look at your answers.

Here are the solutions to questions five and six.

Now, in an exam, you may also be asked a question such as, which are the integer values that satisfy a certain inequality? Now if I were to pick the inequality for six A, X is between negative four and one but not including one, then I could list out all the integers here, there's the integers, and we are excluding the number one so I'm going to cross that out, in fact I can just rub it out like this, and so the integer values that are satisfied by this inequality six A, would be these ones.

Something you might see in an exam.