Step by step
The question
Question: solve 2(x + 3) = 2x + 5.
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.
2 times x is 2x.
2 times 3 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 2x.
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.
2x − 2x = 0.
Now we have 6 = 5.
The x parts are gone.
6 = 5 is never true.
So no number works.
There is no solution.
3 Pick the choice
No solution.
That means zero solutions.
That is choice A.
4 Why not the others
B is exactly one.
Wrong: the x parts cancel: no single x is left to find.
C is exactly two.
Wrong: a line-type equation never has exactly two.
D is infinitely many.
Wrong: 6 = 5 is never true: no number works.
Let's look back.
First: open the brackets.
Then: get x on one side.
Then: pick the choice.
Last: why not the others.