Solve 3x − 5 = 16.

Step by step: way 1, the same on both sides

The question

Question: solve 3x − 5 = 16.

Let's find x.

An equation is like a balance.

Both sides weigh the same.

We want x by itself.

First we remove the − 5, so 3x is alone.

Then we remove the times 3.

Is x alone now?

Not yet: − 5 is still with x.

How do we remove it?

1 Remove the − 5

To remove − 5, we add 5.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

− 5 and + 5 cancel each other.

They make zero.

16 + 5 = 21.

Now we have 3x = 21.

So after step 1: we added 5, and now we have 3x = 21.

Is x alone now?

Not yet: 3x means 3 times x.

2 Remove the 3

To remove times 3, we divide by 3.

We do it on both sides, so they stay equal.

3 divided by 3 is 1.

They cancel each other.

So just x is left.

21 divided by 3 is 7.

So x = 7!

3 Check

Let's check: put 7 in place of x.

Both sides are 16.

The balance is level.

We get 16, the same as the right side.

So x = 7 is right!

Let's look back.

First: remove the − 5.

Then: remove the 3.

Last: check.

Step by step: way 2, the quick way: move it across

The question

Question: solve 3x − 5 = 16.

Let's find x.

We want x by itself.

First we remove the − 5, so 3x is alone.

Then we remove the times 3.

1 Move the − 5 across

The quick way you will see in class: − 5 moves across the = sign and becomes + 5.

It is the same as adding 5 on both sides.

It is only quicker to write.

16 + 5 = 21.

Now we have 3x = 21.

Is x alone now?

Not yet: 3x means 3 times x.

How do we remove it?

2 Remove the 3

To remove times 3, we divide by 3.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

3 divided by 3 is 1.

They cancel each other.

So just x is left.

21 divided by 3 is 7.

So x = 7!

3 Check

Let's check: put 7 in place of x.

We get 16, the same as the right side.

So x = 7 is right!

Let's look back.

First: move the − 5 across.

Then: remove the 3.

Last: check.