Step by step
The question
Question: solve 3x − 7 = 20.
Let's find x.
We want x by itself.
First we remove the − 7, so 3x is alone.
Then we remove the times 3.
There are four choices.
First we solve it, the normal way.
Then we pick.
Is x alone now?
Not yet: − 7 is still with x.
How do we remove it?
1 Remove the − 7
To remove − 7, we add 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.
20 + 7 = 27.
Now we have 3x = 27.
So after step 1: we added 7, and now we have 3x = 27.
Is x alone now?
Not yet: 3x means 3 times x.
2 Remove the 3
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.
27 divided by 3 is 9.
So x = 9!
3 Check
Let's check: put 9 in place of x.
We get 20, the same as the right side.
So x = 9 is right!
4 Pick the choice
Our answer is x = 9.
That is choice B.
5 Why not the others
A is 13/3.
Wrong: took away 7 instead of adding it: 3x = 13.
C is 27.
Wrong: 3x = 27, but we still had to divide by 3.
D is 81.
Wrong: 27 × 3: multiplied instead of dividing.
Let's look back.
First: remove the − 7.
Then: remove the 3.
Then: check.
Then: pick the choice.
Last: why not the others.