Step by step
The question
Question: simplify 3(2x + 1) − 2(x − 5).
Simplify means: write it shorter, with the same value.
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.
Watch the signs.
3 times 2x is 6x.
3 times 1 is 3.
(−2) times x is −2x.
(−2) times (−5) is 10.
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.
Plain numbers go together.
Each colour is one kind.
We move like terms next to each other.
Each term takes its sign with it.
6x − 2x is 4x.
It is like 6 apples take away 2 apples: that is 4 apples.
3 + 10 is 13.
So the expression is 4x + 13.
3 Check
Let's check.
We pick a number for each letter: x = 2.
We put it into the start.
Now into our answer.
Both give 21.
Same value, so 4x + 13 is right!
Let's look back.
First: open the brackets.
Then: group like terms.
Last: check.