Lesson video

Hi, everyone.

I'm Mr. Lund and this lesson is about how we solve equations that first require some simplification.

Hi, everyone.

What equation is represented by the bar model? Here I have 5y and 2y and 28.

All that is equal to 70.

As an equation, I could write that like this.

But what can we do to make solving this equation a little easier? That's right.

We can collect our like terms. Here, 5y + 2y can be simplified to 7y.

This makes solving this equation a lot easier.

Let's go ahead and solve.

If I subtract 28 from both sides of the equation, I can find that 7y is equal to 42.

By dividing both sides of the equation by seven, I solve the equation and y is equal to six.

You can check your answer by substituting six back into your original equation.

What equation is represented by this bar model? This looks far more complicated, but there is a pattern.

Do you see one? Notice 2a and five, 2a and five, 2a and five.

Ahh, that makes three lots of 2a and five.

I could write that like this.

Three lots of 2a + 5 can be displayed as brackets.

Did you notice the 13 on the end? This is all equal to 100.

By expanding my brackets to start, I can find that 6a + 15 + 13 is equal to 100.

Then collect my like terms to simplify our equation.

6a + 28 = 100.

Solve from there.

Subtract 28 from both sides.

6a is equal to 72.

And then divide both sides by six to find the solution a is equal to 12.

Check your answer by substituting the value of 12 into your original equation.

Here are some questions for you to try.

Remember, you first need to expand those brackets and then collect your like terms from there.

Pause the video, come back, check your answers.

Here's the solutions for questions one and number two.

If you want to check your solutions, remember you can substitute them back into the original equation to check that you got the right answer.

Let's try questions three now.

Pause the video and return to check your answers.

Here are the solutions for question three.

Well we know, or hopefully, we found out that Dora was 14 years old.

But what can we say about Amir and Tommy? Well Tommy is half of Dora's age, so he has to be seven, and Amir, when we solved, we found that x was equal to 12, so Amir is 12 years old.

Here's questions four and five.

Questions four involves a lot of negative values, so just be careful when using those.

Pause the video and return when you have finished.

Here are the solutions to questions four and five.

Take care when you have to expand brackets with negative numbers.

I should imagine if people made mistakes on these questions, it is usually when they're expanding.

Here are the final questions.

Well done for getting this far.

Pause the video and return to check your answers.

Here's the solutions to question number six.

I really like this question, it's a nice question.

They are all rearrangements of the same equation.

So you find that y is the same value each time.

It's a nice little question that.