Step by step
The question
Question: solve 3(x − 2) = x + 8.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Open the brackets
The 3 in front of the bracket multiplies every part inside.
So we write 3 times each part.
Watch the signs.
3 times x is 3x.
3 times (−2) is −6.
2 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 1 and 3.
We remove the smaller one, x.
Then the x part that is left is plus.
A plus x part is easier to work with.
So we remove the x from the right side.
To remove x, we take away x.
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.
x and − x make zero.
Cross them out.
3x − x = 2x.
Now we have 2x − 6 = 8.
We want x by itself.
Two things are stuck to x: times 2 and − 6.
First x was times 2.
Then − 6.
To take them off, we go backwards.
First we remove the − 6.
Then the times 2.
3 Remove the − 6
To remove − 6, we add 6.
We do it on both sides, so they stay equal.
− 6 and + 6 make zero.
Cross them out.
8 + 6 = 14.
Now we have 2x = 14.
4 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
14 divided by 2 is 7.
So x = 7!
5 Check
Let's check: put 7 in place of x.
First the left side.
Now the right side.
Both sides are 15.
So x = 7 is right!
6 Pick the choice
Our answer is x = 7.
That is choice D.
7 Why not the others
A is 1.
Wrong: took away 6: 2x = 2.
B is 3.5.
Wrong: added x: 4x = 14.
C is 5.
Wrong: 3x − 2 = x + 8: forgot 3 × 2.
Let's look back.
First: open the brackets.
Then: get x on one side.
Then: remove the − 6.
Then: remove the 2.
Then: check.
Then: pick the choice.
Last: why not the others.