Step by step
The question
Question: if 3x + 12 = 27, what is x + 4?
Sometimes we can find the answer without finding x first.
We want x + 4.
Let's look for it inside the equation.
1 Compare the two
Look at 3x + 12 and x + 4.
We compare them part by part.
3x is 3 times x.
12 divided by 4 is 3.
So 12 is 3 times 4.
Every part of 3x + 12 is 3 times a part of x + 4.
2 Take out the 3
So we can write each part as 3 times.
3 times each part is the same as 3 times the whole bracket: 3(x + 4).
Opening the bracket gives 3x + 12 back.
Is x alone now?
Not yet: 3(x + 4) means 3 times x.
How do we remove it?
3 Remove the 3
3(x + 4) means 3 times the bracket.
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 the bracket is left.
27 divided by 3 is 9.
So x + 4 = 9!
Careful!
Many people find x and stop.
But the question asks for x + 4.
4 Check
Let's check the long way: first we find x.
We want x by itself.
First we remove the + 12, so 3x is alone.
Then we remove the times 3.
Is x alone now?
Not yet: + 12 is still with x.
To remove + 12, we take away 12.
We do it on both sides, so they stay equal.
+ 12 and − 12 cancel each other.
They make zero.
27 − 12 = 15.
Now we have 3x = 15.
3x means 3 times x.
Is x alone now?
Not yet: 3x means 3 times x.
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.
15 divided by 3 is 5.
So x = 5!
Then x + 4 is 5 + 4 = 9.
The same answer.
It works!
5 Type it in
The answer box takes 5 characters.
9 has 1.
It fits.
We type 9.
Let's look back.
First: compare the two.
Then: take out the 3.
Then: remove the 3.
Then: check.
Last: type it in.