Step by step
The question
Question: solve 4(x − 1) − 2x = 2(x + 1).
1 Open the brackets
What is in front of a bracket multiplies every part inside.
So we write each part times what is in front.
Work out each multiplication.
2 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
4x − 2x = 2x.
Now we have 2x − 4 = 2x + 2.
3 Get x on one side
There is x on both sides.
We want x on one side only.
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 −4 = 2.
The x parts are gone.
−4 = 2 is never true.
So no number works.
There is no solution.
Let's look back.
First: open the brackets.
Then: group like terms.
Last: get x on one side.