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Hi, my name's Mrs. Dunnett.

In this lesson, we're going to be solving equations involving a function of X.

Here we're given a function of X is equal to five X, and we're going to use this to solve the fine equations.

So I'm part A.

We've got a function of X is equal to 35.

We know that our function of X is five X, so we can write five X equals 35, and we then use, inverse operations to solve this equation to find the value of X.

Just like you would do with any normal linear equation.

So we're going to divide both sides by five and we get X is equal to seven.

Let's have a look at part B.

This time we've got function of X is equal to negative 10.

So again, we got five X equals negative 10.

So our function of X is equal to negative 10.

We divided by five and we get X equals negative two.

Part C we've got our function of X is equal to 1.

6 and probably getting the hang of this now.

So we write five X equals 1.

6.

Use inverse operations to solve.

So we're going to divide by five and we get X is equal to 0.

32.

And finally, we've got function of X equal to three.

So we've got five X is equal to three, divide both sides by five and we get X is equal to three fifths.

Or you can write that answer as a decimal if you want.

So the answer is X is equal to three fifths.

Here's some equations for you to solve.

Pause the video, to complete the questions and restart when you have finished.

Here are the answers.

All we had to do here was divided by three to get the value for X in each question.

We've now got a different function of X.

This time, our function of X is equal to five X plus two.

And we're going to solve the following equation.

So for our first equation, we've got function of X is equal to 32.

So we're at five X plus two equals 32.

And we use inverse operations to solve this.

So the first thing we need to do, is subtract two from both sides.

We get five X equals 30, and then we divide both sides by five to find X is equal to six.

In the next question we've got function of X is equal to 18.

So we're at five X plus two equals 18.

Again, use inverse operation, subtract in two and divided by five, to get X is equal to 16 over five.

Now we can leave this answer as a fraction.

We could change it into a mixed number, if you wanted, or even a decimal, it's entirely up to you.

Just make sure you do it very accurately, if you're going to change it, into a decimal.

And next up we've got function of X is equal to negative eight.

So we write five X plus two equals negative eight.

We're going to subtract two from both sides.

Negative eight, take away two is negative ten.

So we're moving further away from zero.

And then we divide by five and we get X is equal to negative two.

And finally, we've got a function of X is equal to five.

So for this question, we do the same again.

We write our function of X equal to five, and we solve it, using inverse operations.

So we subtract two, divided by five and we get an answer of X is equal to 0.

6, or we could write that as a fraction if we wanted to.

So that will be X is equal to three fifths.

Here's some equations for you to solve.

Pause the video, complete the questions and restart when you have finished.

Here are the answers.

This time you should have been using the inverse operations, add three and divide by five to solve.

Now we're going to look at a quadratic equation.

So we've got our function of X this time has got a squared term in it, and we're going to solve the following equations.

So for the first one, we want our function of X to equal 12.

So the function of X is three X squared, and we put that equal to 12 and we then solve it using inverse operations.

You have to be very careful here to remember, that if we multiply X by itself, X squared, we then times it my three.

So we're doing the inverse of that.

So the first thing we're going to do is we're going to divide by three.

And we get X squared is equal to four, and then we square root four and we get X is equal to positive or negative two.

So we're getting two solutions there because we've got a quadratic equation.

For the next question, we've got F of X is equal to 1.

92.

So we write our function of X, three X squared equal to 1.

92, and we use inverse operations to solve.

So I divide by three, to get X squared is equal to 0.

64.

Square root it.

And we get X is equal to positive or negative 0.

8.

And we could leave that as a fraction if we wanted to.

But as the question is given in decimals, it makes more sense to leave our answer as X equals a plus or minus 0.

8.

Here are some questions for you to try.

Pause the video to complete the task and restart when you've finished.

Here are the answers.

Notice that there are two solutions for each question as our equations are quadratic.

So we get a positive and a negative solution.

Our next function of X involves a fraction.

So we've got our function of X is equal to three X take away nine, all divided by two.

And we want to solve this equation when function of X is equal to 18.

So we write our function of X equal to 18.

Just as we've been doing with all the previous examples.

And then we need to think about, how we're going to solve this equation.

So hopefully you've got some experience of solving fractional equations prior to this lesson.

And you'll see, the first thing you want to do really is to get rid of that, dividing by two.

So we're going to multiply both sides by two.

And that gets rid of that fraction on the left hand side of the equation, and we get 36 on the right hand side of the equation.

And then we add nine to both sides and divide by three.

And we get X is equal to 15.

Let's have a look at these two functions now.

So this time we've got a function of X and a function G of X.

So you can see we've got two different functions here, and we want to solve the equation, F of X equals G of X.

So we have to equate these two functions.

So we put 10X minus four is equal to eight minus five X, and then we start to solve this equation to find the value of X.

So the first thing I'm going to do is add five X to both sides.

You could of course, add four to both sides, if you wish, it doesn't really matter here.

But we'll start off by adding five X to both sides.

And we get 15X tech where four is eight.

Add four to each side of the equation and we get 15X equals 12, and then we divide by 15 and we get X is equal to four fifths when simplified.

Here are two final questions for you to try.

Pause the video to complete each one and restart when you have finished.

Here are the answers.

If you wrote your answers as fractions equivalent to the decimal shown, then that is also correct.

That's all for this lesson.

Remember to take the exit quiz before you leave.

Thank you for watching.