Step by step
The question
Question: solve 3(x − 2) + 4 = x + 10.
1 Open the brackets
The 3 in front of the bracket multiplies every part inside.
So we write 3 times each part.
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.
−6 + 4 = −2.
Now we have 3x − 2 = x + 10.
3 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the x from the right side.
To remove x, we take away x.
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.
x and − x make zero.
Cross them out.
3x − x = 2x.
Now we have 2x − 2 = 10.
We want x by itself.
Two things are stuck to x: times 2 and − 2.
The − 2 is on the outside, so it comes off first.
Then the times 2.
4 Remove the − 2
To remove − 2, we add 2.
We do it on both sides, so they stay equal.
− 2 and + 2 make zero.
Cross them out.
10 + 2 = 12.
Now we have 2x = 12.
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.
12 divided by 2 is 6.
So x = 6!
6 Check
Let's check: put 6 in place of x.
First the left side.
Now the right side.
Both sides are 16.
So x = 6 is right!
Let's look back.
First: open the brackets.
Then: group like terms.
Then: get x on one side.
Then: remove the − 2.
Then: remove the 2.
Last: check.