Step by step
The question
Question: solve x/4, + 2 = 5.
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 2 and 5 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 2 is 8.
4 times 5 is 20.
No more fractions!
2 Remove the + 8
We want x by itself.
The + 8 is in the way.
To remove + 8, we take away 8.
We do it on both sides, so they stay equal.
+ 8 and − 8 make zero.
Cross them out.
20 − 8 = 12.
So x = 12!
3 Check
Let's check: put 12 in place of x.
We get 5, the same as the right side.
So x = 12 is right!
4 Pick the choice
Our answer is x = 12.
That is choice B.
5 Why not the others
A is 3/4.
Wrong: x/4 = 3, then divided 3 by 4.
C is 18.
Wrong: x + 2 = 20: multiplied only the 5 by 4.
D is 28.
Wrong: added 2: x/4 = 7.
Let's look back.
First: remove the fraction.
Then: remove the + 8.
Then: check.
Then: pick the choice.
Last: why not the others.