Step by step
The question
Question: solve 2(x − 4) = 3x + 1.
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Open the brackets
The 2 in front of the bracket multiplies every part inside.
So we write 2 times each part.
Watch the signs.
2 times x is 2x.
2 times (−4) is −8.
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 2 and 3.
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 left 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.
3x − 2x = x.
Now we have −8 = x + 1.
Let's swap the two sides, so x is on the left.
Both sides are the same amount, so we can swap them.
3 Remove the + 1
We want x by itself.
The + 1 is in the way.
To remove + 1, we take away 1.
We do it on both sides, so they stay equal.
+ 1 and − 1 make zero.
Cross them out.
−8 − 1 = −9.
So x = −9!
4 Check
Let's check: put −9 in place of x.
First the left side.
Now the right side.
Both sides are −26.
So x = −9 is right!
5 Pick the choice
Our answer is x = −9.
That is choice A.
6 Why not the others
B is −5.
Wrong: 2x − 4 = 3x + 1: forgot 2 × 4.
C is 9/5.
Wrong: moved 3x without changing its sign: 5x = 9.
D is 9.
Wrong: lost the minus sign.
Let's look back.
First: open the brackets.
Then: get x on one side.
Then: remove the + 1.
Then: check.
Then: pick the choice.
Last: why not the others.