Step by step
The question
Question: solve x/2 + x/3 = 10.
1 Remove the fractions
The bottom numbers are 2 and 3.
6 can be divided by all of them.
We multiply every part by 6.
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.
6 divided by 2 is 3.
6 divided by 3 is 2.
Write what is left.
Do the multiplications.
No more fractions!
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.
3x + 2x = 5x.
Now we have 5x = 60.
3 Remove the 5
5x means 5 times x.
We want just x.
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
So just x is left.
60 divided by 5 is 12.
So x = 12!
4 Check
Let's check: put 12 in place of x.
We get 10, the same as the right side.
So x = 12 is right!
Let's look back.
First: remove the fractions.
Then: group like terms.
Then: remove the 5.
Last: check.