Step by step
The question
Question: solve 4x + 9 = 33.
Let's find x.
We want x by itself.
First we remove the + 9, so 4x is alone.
Then we remove the times 4.
There are four choices.
First we solve it, the normal way.
Then we pick.
Is x alone now?
Not yet: + 9 is still with x.
How do we remove it?
1 Remove the + 9
To remove + 9, we take away 9.
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.
+ 9 and − 9 cancel each other.
They make zero.
33 − 9 = 24.
Now we have 4x = 24.
So after step 1: we took away 9, 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.
We get 33, the same as the right side.
So x = 6 is right!
4 Pick the choice
Our answer is x = 6.
That is choice A.
5 Why not the others
B is 21/2.
Wrong: added 9: 4x = 42.
C is 24.
Wrong: 4x = 24, but we still had to divide by 4.
D is 96.
Wrong: 24 × 4: multiplied instead of dividing.
Let's look back.
First: remove the + 9.
Then: remove the 4.
Then: check.
Then: pick the choice.
Last: why not the others.