Step by step
The question
Question: solve 4x − 7 = 21.
We want x by itself.
Two things are stuck to x: times 4 and − 7.
First x was times 4.
Then − 7.
To take them off, we go backwards.
First we remove the − 7.
Then the times 4.
There are four choices.
First we solve it, the normal way.
Then we pick.
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 make zero.
Cross them out.
21 + 7 = 28.
Now we have 4x = 28.
2 Remove the 4
4x means 4 times x.
We want just x.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just x is left.
28 divided by 4 is 7.
So x = 7!
3 Check
Let's check: put 7 in place of x.
We get 21, the same as the right side.
So x = 7 is right!
4 Pick the choice
Our answer is x = 7.
That is choice B.
5 Why not the others
A is 3.5.
Wrong: took away 7: 4x = 14.
C is 28.
Wrong: 4x = 28, but we still had to divide by 4.
D is 112.
Wrong: 28 × 4: multiplied instead of dividing.
Let's look back.
First: remove the − 7.
Then: remove the 4.
Then: check.
Then: pick the choice.
Last: why not the others.