Step by step
The question
Question: if 3x + 6 = 21, what is x + 2?
We want x + 2.
Let's look for it inside the equation.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Compare the two
Look at 3x + 6 and x + 2.
We compare them part by part.
3x is 3 times x.
6 divided by 2 is 3.
So 6 is 3 times 2.
Every part of 3x + 6 is 3 times a part of x + 2.
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 + 2).
Opening the bracket gives 3x + 6 back.
3 Remove the 3
3(x + 2) 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.
So just the bracket is left.
21 divided by 3 is 7.
So x + 2 = 7!
Careful!
Many people find x and stop.
But the question asks for x + 2.
4 Check
Let's check the long way: first we find x.
We want x by itself.
Two things are stuck to x: times 3 and + 6.
First x was times 3.
Then + 6.
To take them off, we go backwards.
First we remove the + 6.
Then the times 3.
To remove + 6, we take away 6.
We do it on both sides, so they stay equal.
+ 6 and − 6 make zero.
Cross them out.
21 − 6 = 15.
Now we have 3x = 15.
3x means 3 times x.
We want just 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.
So just x is left.
15 divided by 3 is 5.
So x = 5!
Then x + 2 is 5 + 2 = 7.
The same answer.
It works!
5 Pick the choice
Our answer is x + 2 = 7.
That is choice B.
6 Why not the others
A is 5.
Wrong: that is x, not x + 2.
That is the Careful mistake from before.
C is 15.
Wrong: that is 3x, not x + 2.
D is 21.
Wrong: that is 3x + 6, not x + 2.
Let's look back.
First: compare the two.
Then: take out the 3.
Then: remove the 3.
Then: check.
Then: pick the choice.
Last: why not the others.