Step by step
The question
Question: solve 5x − 3 = 2x + 12.
Let's find x.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Get x on one side
There is x on both sides.
We want x on one side only.
The numbers in front of x are 2 and 5.
We remove the smaller one, 2x, so the x part that is left is plus.
So we remove the 2x from the right side.
To remove 2x, we take away 2x.
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.
2x and − 2x cancel each other.
They make zero.
5x − 2x = 3x.
Now we have 3x − 3 = 12.
We want x by itself.
First we remove the − 3, so 3x is alone.
Then we remove the times 3.
So after step 1: we took away 2x, and now we have 3x − 3 = 12.
Is x alone now?
Not yet: − 3 is still with x.
How do we remove it?
2 Remove the − 3
To remove − 3, we add 3.
We do it on both sides, so they stay equal.
− 3 and + 3 cancel each other.
They make zero.
12 + 3 = 15.
Now we have 3x = 15.
So after step 2: we added 3, and now we have 3x = 15.
Is x alone now?
Not yet: 3x means 3 times x.
3 Remove the 3
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
They cancel each other.
So just x is left.
15 divided by 3 is 5.
So x = 5!
4 Check
Let's check: put 5 in place of x.
First the left side.
Now the right side.
Both sides are 22.
So x = 5 is right!
5 Pick the choice
Our answer is x = 5.
That is choice C.
6 Why not the others
A is 9/7.
Wrong: added 2x: 7x = 9.
B is 3.
Wrong: took away 3: 3x = 9.
D is 15.
Wrong: 3x = 15, but we still had to divide by 3.
Let's look back.
First: get x on one side.
Then: remove the − 3.
Then: remove the 3.
Then: check.
Then: pick the choice.
Last: why not the others.