Solve 4x + 7 = 31.

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

The question

Question: solve 4x + 7 = 31.

Let's find x.

An equation is like a balance.

Both sides weigh the same.

We want x by itself.

First we remove the + 7, so 4x is alone.

Then we remove the times 4.

Is x alone now?

Not yet: + 7 is still with x.

How do we remove it?

1 Remove the + 7

To remove + 7, we take away 7.

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.

+ 7 and − 7 cancel each other.

They make zero.

31 − 7 = 24.

Now we have 4x = 24.

So after step 1: we took away 7, and now we have 4x = 24.

Is x alone now?

Not yet: 4x means 4 times x.

2 Remove the 4

To remove times 4, we divide by 4.

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

4 divided by 4 is 1.

They cancel each other.

So just x is left.

24 divided by 4 is 6.

So x = 6!

3 Check

Let's check: put 6 in place of x.

Both sides are 31.

The balance is level.

We get 31, the same as the right side.

So x = 6 is right!

Let's look back.

First: remove the + 7.

Then: remove the 4.

Last: check.

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

The question

Question: solve 4x + 7 = 31.

Let's find x.

We want x by itself.

First we remove the + 7, so 4x is alone.

Then we remove the times 4.

1 Move the + 7 across

The quick way you will see in class: + 7 moves across the = sign and becomes − 7.

It is the same as taking away 7 on both sides.

It is only quicker to write.

31 − 7 = 24.

Now we have 4x = 24.

Is x alone now?

Not yet: 4x means 4 times x.

How do we remove it?

2 Remove the 4

To remove times 4, we divide by 4.

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.

4 divided by 4 is 1.

They cancel each other.

So just x is left.

24 divided by 4 is 6.

So x = 6!

3 Check

Let's check: put 6 in place of x.

We get 31, the same as the right side.

So x = 6 is right!

Let's look back.

First: move the + 7 across.

Then: remove the 4.

Last: check.