Solve 7x − 3 = 2x + 22.

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

The question

Question: solve 7x − 3 = 2x + 22.

Let's find x.

1 Get x on one side

There is x on both sides.

We want x on one side only.

The numbers in front of x are 2 and 7.

We remove the smaller one, 2x, so the x part that is left is plus.

So we remove the 2x from the right side.

To remove 2x, we take away 2x.

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.

2x and − 2x cancel each other.

They make zero.

7x − 2x = 5x.

Now we have 5x − 3 = 22.

We want x by itself.

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

Then we remove the times 5.

So after step 1: we took away 2x, and now we have 5x − 3 = 22.

Is x alone now?

Not yet: − 3 is still with x.

How do we remove it?

2 Remove the − 3

To remove − 3, we add 3.

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

− 3 and + 3 cancel each other.

They make zero.

22 + 3 = 25.

Now we have 5x = 25.

So after step 2: we added 3, and now we have 5x = 25.

Is x alone now?

Not yet: 5x means 5 times x.

3 Remove the 5

To remove times 5, we divide by 5.

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

5 divided by 5 is 1.

They cancel each other.

So just x is left.

25 divided by 5 is 5.

So x = 5!

4 Check

Let's check: put 5 in place of x.

First the left side.

Now the right side.

Both sides are 32.

So x = 5 is right!

Let's look back.

First: get x on one side.

Then: remove the − 3.

Then: remove the 5.

Last: check.

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

The question

Question: solve 7x − 3 = 2x + 22.

Let's find x.

1 Get x on one side

There is x on both sides.

We want x on one side only.

The numbers in front of x are 2 and 7.

We remove the smaller one, 2x, so the x part that is left is plus.

So we remove the 2x from the right side.

To remove 2x, we take away 2x.

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.

2x and − 2x cancel each other.

They make zero.

7x − 2x = 5x.

Now we have 5x − 3 = 22.

We want x by itself.

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

Then we remove the times 5.

So after step 1: we took away 2x, and now we have 5x − 3 = 22.

2 Move the − 3 across

The quick way you will see in class: − 3 moves across the = sign and becomes + 3.

It is the same as adding 3 on both sides.

It is only quicker to write.

22 + 3 = 25.

Now we have 5x = 25.

Is x alone now?

Not yet: 5x means 5 times x.

How do we remove it?

3 Remove the 5

To remove times 5, we divide by 5.

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

5 divided by 5 is 1.

They cancel each other.

So just x is left.

25 divided by 5 is 5.

So x = 5!

4 Check

Let's check: put 5 in place of x.

First the left side.

Now the right side.

Both sides are 32.

So x = 5 is right!

Let's look back.

First: get x on one side.

Then: move the − 3 across.

Then: remove the 5.

Last: check.