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Hello, my name's Miss Parnham.

In this lesson, we're going to be solving equations with brackets.

Let's solve this equation and we'll use a function machine to demonstrate the order in which we apply the inverse functions to solve it.

So a has four subtracted from it.

Then all that is multiplied by three and the solution is -21.

So to find the value of a, we must reverse that process.

So to the equation, we're dividing both sides by three, so a - 4 = -7.

And then we're adding four so that a = -3.

We can do something similar with a worded problem.

Here we can see in this worded problem, we have the keywords of adds and divides.

So Jack adds five sweets to a bag, so that's going to be b + 5.

He then divides the sweets into seven equal piles of four.

So he's dividing by seven.

The vinculum must go all the way underneath the expression b + 5 to show all of that is being divided by seven and that's equal to four.

So five is added to b, it's divided by seven and the answer is four.

Let's reverse that process by using the inverse functions.

So we're multiplying both sides by seven so that b + 5 is 28.

And then we're subtracting five so that b is 23.

Here are some questions for you to try.

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

Here are the answers.

In question two, notice that the vinculum stretches all the way underneath the expression of n - 5.

That's because we want to group it together and divide it all by three.

Here are some more questions for you to try.

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

Here are the answers.

In question four, we look at two ways to solve the same equation.

If you prefer to expand the bracket first, that's fine.

As you can see, you would still get the same solution.

You just do whatever you're most comfortable with.

Now let's try solving equations that involve decimals in exactly the same way.

So c has five added to it, then it's multiplied by eight and the answer is 73.

6.

So we need to divide by eight, both sides of the equation, that gives us c + 5 = 9.

2.

We subtract five, so c is 4.

2.

In this example, 7.

4 is subtracted from d and then all of that is divided by four.

As you can see the vinculum goes all the way underneath that expression and the answer is -4.

65.

So let's reverse that process.

Let's multiply both sides by four, so d - 7.

4 is -18.

6.

Let's add 7.

4 to both sides so d is -11.

2.

Here are some questions for you to try.

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

Here are the answers.

Questions five and six have decimal solutions but if you have given equivalent fractional, or mixed number solutions, they're just as valid.

Here are some further questions for you to try.

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

Here are the answers.

Question seven is associated with money and if we have an amount with a zero in the second decimal place, then we're not require to put that into the equation.

But do remember when we have a solution, for example we have 3.

8 here, when we give our final answer, that must have two decimal places so there we have the answer three pounds 80.

In question eight, you needed to remember the formula for the area of a triangle.

So that's height times base and divide by two.

And you should have got the answer 8.

2.

Sometimes a question might ask for the height, so you might have to substitute a value that you find for a letter back in and then give a final answer.

So in this case you would do 8.

2, subtract five, and you would get 3.

2.

That's all for this lesson.

Thank you for watching.