Step by step
The question
Question: if 4y + 12 = 20, what is y + 3?
We want y + 3.
Let's look for it inside the equation.
1 Compare the two
Look at 4y + 12 and y + 3.
We compare them part by part.
4y is 4 times y.
12 divided by 3 is 4.
So 12 is 4 times 3.
Every part of 4y + 12 is 4 times a part of y + 3.
2 Take out the 4
So we can write each part as 4 times.
4 times each part is the same as 4 times the whole bracket: 4(y + 3).
Opening the bracket gives 4y + 12 back.
3 Remove the 4
4(y + 3) means 4 times the bracket.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just the bracket is left.
20 divided by 4 is 5.
So y + 3 = 5!
Careful!
Many people find y and stop.
But the question asks for y + 3.
4 Check
Let's check the long way: first we find y.
We want y by itself.
Two things are stuck to y: times 4 and + 12.
First y was times 4.
Then + 12.
To take them off, we go backwards.
First we remove the + 12.
Then the times 4.
To remove + 12, we take away 12.
We do it on both sides, so they stay equal.
+ 12 and − 12 make zero.
Cross them out.
20 − 12 = 8.
Now we have 4y = 8.
4y means 4 times y.
We want just y.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just y is left.
8 divided by 4 is 2.
So y = 2!
Then y + 3 is 2 + 3 = 5.
The same answer.
It works!
Let's look back.
First: compare the two.
Then: take out the 4.
Then: remove the 4.
Last: check.