Step by step
The question
Question: solve 2(x + 3) = 14.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Remove the 2
The 2 multiplies the whole bracket.
Easy way: remove the 2 first.
Then we do not have to open the bracket.
To remove times 2, we divide by 2.
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.
2 divided by 2 is 1.
So just the bracket is left.
14 divided by 2 is 7.
Now we have x + 3 = 7.
We don't need the bracket any more.
2 Remove the + 3
We want x by itself.
The + 3 is in the way.
To remove + 3, we take away 3.
We do it on both sides, so they stay equal.
+ 3 and − 3 make zero.
Cross them out.
7 − 3 = 4.
So x = 4!
3 Check
Let's check: put 4 in place of x.
We get 14, the same as the right side.
So x = 4 is right!
4 Pick the choice
Our answer is x = 4.
That is choice A.
5 Why not the others
B is 5.5.
Wrong: 2x + 3 = 14: forgot 2 × 3.
C is 10.
Wrong: added 6: 2x = 20.
D is 11.
Wrong: x + 3 = 14: forgot the 2.
Let's look back.
First: remove the 2.
Then: remove the + 3.
Then: check.
Then: pick the choice.
Last: why not the others.