Step by step
The question
Question: solve 3 − 2(x − 1) = 4(2 − x).
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.
Plain numbers go together.
3 + 2 = 5.
Now we have 5 − 2x = 8 − 4x.
3 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the −4x from the right side.
To remove −4x, we add 4x.
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.
− 4x and + 4x make zero.
Cross them out.
−2x + 4x = 2x.
Now we have 5 + 2x = 8.
We want x by itself.
Two things are stuck to x: times 2 and + 5.
The + 5 is on the outside, so it comes off first.
Then the times 2.
4 Remove the 5
To remove 5, we take away 5.
We do it on both sides, so they stay equal.
5 and − 5 make zero.
Cross them out.
8 − 5 = 3.
Now we have 2x = 3.
5 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.
So x = 3/2!
6 Check
Let's check: put 3/2 in place of x.
First the left side.
Now the right side.
Both sides are 2.
So x = 3/2 is right!
Let's look back.
First: open the brackets.
Then: group like terms.
Then: get x on one side.
Then: remove the 5.
Then: remove the 2.
Last: check.