Step by step
The question
Question: solve 5x − 3 = 2x + 9.
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.
Then the x part that is left is plus.
A plus x part is easier to work with.
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 make zero.
Cross them out.
5x − 2x = 3x.
Now we have 3x − 3 = 9.
We want x by itself.
Two things are stuck to x: times 3 and − 3.
First x was times 3.
Then − 3.
To take them off, we go backwards.
First we remove the − 3.
Then the times 3.
2 Remove the − 3
To remove − 3, we add 3.
We do it on both sides, so they stay equal.
− 3 and + 3 make zero.
Cross them out.
9 + 3 = 12.
Now we have 3x = 12.
3 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
12 divided by 3 is 4.
So x = 4!
4 Check
Let's check: put 4 in place of x.
First the left side.
Now the right side.
Both sides are 17.
So x = 4 is right!
5 Pick the choice
Our answer is x = 4.
That is choice C.
6 Why not the others
A is 12/7.
Wrong: added 2x: 7x = 12.
B is 2.
Wrong: took away 3: 3x = 6.
D is 12.
Wrong: 3x = 12, 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.