Lesson video

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Hi everyone, I'm Mr. Lund.

In this lesson, we're going to be solving inequalities, which involve algebraic fractions.

Hi everyone, we solve inequalities, in much the same way, that we solve equations.

Here I have an inequality, which involves an algebraic fraction.

A over two, is less than 1.


To solve this inequality, the first step I need to take, is to multiply both sides by two.

That will find me, a is less than three.

I could represent that on a number line, like so.

What's the same and what's different with this example? Here, the inequality symbol is different, and we have a negative number.

Let's follow the same path as previously.

We're going to multiply both sides by two.

A is less than or equal to negative two.

Multiplying a positive and a negative number, by achieving negative solution, I can represent this inequality, on a number line, like so.

Don't get too worried, if it seems like the unknown is on the wrong side of the inequality.

Follow the same steps as previously.

In this case, one is greater than a divided by three.

So I'm going to multiply both sides of this inequality by three this time.

That finds me that three is greater than a.

Now, that can also be written as, a is less than three, they mean the same thing.

Here's how it would be represented on a number line.

Here are some inequalities involving fractions for you to try.

Pause the video and return to check your answers.

Here is the solutions to question number one.

The final question, is basically saying, a half of a plus a half of eight is less than four.

So that means that, a, is less than four we collect our like terms. Why not try questions two and three? Pause the video, return and check your answers.

Here's the solutions question two, and three.

Don't make the mistake of adding an equal sign when you are using inequalities.

Let's solve this two step inequality.

The first thing I'm going to do here, is subtract one from both sides.

Don't make the mistake of multiplying everything through by two at this stage.

That will make your life a little more complex.

By subtracting one from both sides of the inequality, I can find that, a over two is greater than four, then, you can multiply both sides by two, to find a greater than eight.

Have a look at this example.

what's the same and what's different? In this example, the first step you should take is to multiply both sides by two.

Don't forget, to multiply, the five by two to give you 10, and the fraction to give you the numerator of a plus one.

Solve by subtracting one from both sides, finds you inequality a greater than nine.

So here are some questions for you try.

Pause the video and return to check your answers.

Here's the solutions to questions four and five.

Try not to get these examples of different fractions confused, they are not the same.

Well done for getting this far.

Here's questions six and seven.

Pause video and return to check your answers.

Here are the solutions to question six and seven.

So, for question six a, a over three plus two is greater than six.

If you have multiplied first of all everything by three, to find that a plus six is greater than 18, then you would find the correct solutions, but, it is easier to subtract two from both sides to start.