Lesson video

Ooh.

Hi, everyone.

I'm Mr. Lund.

This lesson is about solving one- and two-step inequalities.

Let's solve some inequalities.

Here I have the inequality x plus one is greater than six.

You can solve inequalities in the same way that you solve equations.

If I subtract one from both sides of this inequality, I could find that x is greater than five.

Look at this second example.

Here we have a negative three rather than a positive one.

And also the inequality symbol is less than or equal to rather than greater than in the last example.

To solve this inequality, add three to both sides of the inequality and find that x is less than or equal to six.

To solve this inequality, you would have to subtract seven from both sides.

What would your answer be? There you go.

X is less than or equal to negative seven.

Here are some more examples.

We can solve inequalities in the same way that we solve equations.

Three x is greater than negative 15.

If I divide both sides by three, I can find the solution for x.

X is greater than negative five.

Have a look at this example.

What's same and what's different? Well, we can see the inequality is different.

But the three x is the same and we have a positive five.

To solve this inequality, I can divide both sides by three again.

Five divided by three gives me a recurring decimal answer.

So I can write x is less than or equal to five over three to make my solution far neater than having to write a recurring decimal.

In algebra, writing fractions as your solution, it's very common and it's something you should get used to doing.

Let's have another quickfire example.

Solve four x is less than or equal to negative 16.

Here, x is less than or equal to negative four.

Solve four x is less than or equal to five.

From the number cards below, can you find the answer? There we go.

X is less than or equal to five over four, which is the same as saying X is less than or equal to 1.

25.

Here are some inequalities for you to solve.

Pause the video and come back when you want to check your answers.

Here's the solutions to question number one.

Question one, g, you first have to collect like terms and then divide by five to find the solution.

You could have left your solution as a fraction or a decimal.

In algebra, it is common practise to leave your solution as a fraction.

Let's try questions two and three now.

Pause the video and come back to check your answers.

Here's the solutions to questions number two and three.

Now, in question three, because we're so used to using equal sign, it is a common mistake to place an equal sign when we complete working out our inequalities or solving our inequalities.

Just watch out for that mistake.

Let's go ahead and solve some two-step inequalities.

Here are some examples for you.

The first step I need to take, much like if you were solving an equation, is subtracting one from both sides of this inequality.

That will leave me with two x is greater than 14.

To find the values of x, I divide both sides by two, and x is greater than seven.

Have a look at this example.

Oh no, it looks like the variables are on the other side of the inequality.

But that's fine.

We can just follow the same pattern as previously.

But oh no, there's a negative six there.

Don't worry.

Let's add six to both sides.

That will find me 10 is less than or equal to two x.

Let's divide both sides by two.

And I will find that five is less than or equal to x.

You could also write this to be X is greater than or equal to five.

If you flip the inequality, then you also have to flip the sign.

Technical language there for you.

Let's brighten up our lives with one last example.

We're going to expand and solve.

Here we go.

First of all, expand our brackets out.

That means multiply everything inside the brackets by two.

That would give us two x plus two is less than 10.

Subtract two from both sides of the inequality, giving you two x is less than eight.

And finally divide both sides of the inequality by two finding you solution's x is less than four.

Here are some inequalities for you to solve.

Pause the video and come back to check your answers.

Here's the solutions to questions four and five.

So, Max says, correctly, that both of those inequalities are the same.

And they are.

You have to solve the first one, which said three y plus one is less than four, solving that, y is less than one.

Now, if y is less than one, that means that one is greater than Y.

Have a think about that.

Here are some inequalities that you first need to expand before solving.

Pause the video and come back when you check your answers.

Here's the solutions for question six and seven.

How did you do? Well done for getting this far.

You're getting on to some more complicated examples.

In question six a and b, you have to expand both of those brackets, but did you notice that both the brackets equal zero? How does that help you quickly solve those inequalities? Have a think.