Step by step
The question
Question: solve x/4, + 3 = 7.
Let's find x.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Remove the fraction
The bottom number is 4.
A fraction means divide: x/4 is x divided by 4.
To remove divided by 4, we multiply by 4.
We multiply every part by 4, not only the fraction.
Each whole side is times 4, so 3 and 7 are times 4 too.
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.
4 divided by 4 is 1.
The bottom is gone.
We write it again, without the crossed-out parts.
4 times 3 is 12.
4 times 7 is 28.
No more fractions!
Is x alone now?
Not yet: + 12 is still with x.
How do we remove it?
2 Remove the + 12
We want x by itself.
The + 12 is in the way.
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.
28 − 12 = 16.
So x = 16!
3 Check
Let's check: put 16 in place of x.
We get 7, the same as the right side.
So x = 16 is right!
4 Pick the choice
Our answer is x = 16.
That is choice B.
5 Why not the others
A is 1.
Wrong: 7 − 3 = 4, then divided by 4: to undo ÷ 4 we multiply by 4.
C is 25.
Wrong: multiplied 7 by 4 but not the 3.
D is 40.
Wrong: added 3 instead of taking it away: 10 × 4.
Let's look back.
First: remove the fraction.
Then: remove the + 12.
Then: check.
Then: pick the choice.
Last: why not the others.