Lesson video

Hello, my name is Miss Parnham.

In this lesson, we're going to learn how to solve equations with unknown on both sides.

Let's solve this equation using the balance method, which means doing the same to both sides of the equation.

Because we have two terms that involve e and we only require one, we must eliminate the smaller one.

So let's subtract three e from both sides of the equation.

And that simplifies to five e subtract five equals 10.

Now let's eliminate the subtract five.

We do that by adding five.

That gives us five e equals 15.

To get e on its own, all we need to do now is divide by five.

So e is three.

We can form equations from problems. If we have a rectangle, and we know that the opposite sides on a rectangle are equal.

So we can take these two expressions to form an equation.

Just like before, we eliminate the smaller of the two unknowns.

Let's subtract five f.

So five equals five f subtract seven.

Let's eliminate the subtract seven by adding seven.

So 12 equals five f.

Now let's divide by five.

2.

4 equals f or if you prefer f equals 2.

4.

Here's 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, we have a parallelogram.

We just opposite equal angles.

So setting the two expressions equal to one another, forms an equation which we can solve.

Here's 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 have an isosceles triangle as indicated by the markings, which means the sides are the same length.

So three n plus four equals seven n plus six, forms the equation that we can solve.

Let's solve this equation.

You'll notice now we have brackets.

In this instance, we really need to multiply those brackets out.

So let's rewrite this as three g subtract 12 equals five g plus eight.

Now we can eliminate the smallest g.

Let's subtract it.

Negative 12 equals two g plus eight.

Let's subtract eight in order to eliminate the add eight.

So negative 20 equals two g.

Let's divide by two.

Negative 10 equals g, or if you prefer g equals negative 10.

Let's look at this problem.

These rectangles have the same area.

So four multiplied by two h subtract one, equals three multiplied by three h subtract three.

We need to multiply these brackets out.

So eight h subtract four equals nine h subtract nine.

Let's eliminate the smallest unknown.

Let's subtract eight h.

So negative four equals h subtract nine.

Let's add nine to eliminate the subtract nine.

So five equals h or h equals five.

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 six, we have a pair of corresponding angles, which are equal.

So setting the two expressions equal to one another, forms an equation that can be solved to find z.

Here's another question for you to try.

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

Here are the answers.

In this question, we have regular polygons, which means the sides on each polygon are equal.

So the Pentagon has obviously got five sides, and that's why we have five outside the bracket containing five v subtract three.

Hexagon has six sides, six outside the bracket containing three v plus one, and we solve to find v is three.

That's all for this lesson.

Thank you for watching.