Step by step
The question
Question: solve 3(x + 2) = 3x + 6.
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.
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.
Both x parts are 3x.
So we remove the 3x from the right side.
To remove 3x, we take away 3x.
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.
3x and − 3x make zero.
Cross them out.
3x − 3x = 0.
Now we have 6 = 6.
The x parts are gone.
6 = 6 is always true.
So every number works!
3 Pick the choice
Every number works.
That means infinitely many solutions.
That is choice D.
4 Why not the others
A is zero.
Wrong: 6 = 6 is always true: every number works.
B is exactly one.
Wrong: the x parts cancel: every x works, not one.
C is exactly two.
Wrong: a line-type equation never has exactly two.
Let's look back.
First: open the brackets.
Then: get x on one side.
Then: pick the choice.
Last: why not the others.