Step by step
The question
Question: are 4x + 2x and 6x equivalent?
4x + 2x and 6x
Equivalent means: the two are equal, whatever number the letter is.
equivalent = equal for every number
First we simplify the first one: 4x + 2x.
We write it shorter, with the same value.
= 4x + 2x
1 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.
Each colour is one kind.
like terms = same letters,
same powers
4x + 2x is 6x.
It is like 4 apples plus 2 apples: that is 6 apples.
4x + 2x = 6x
So the expression is 6x.
= 6x
2 Compare
Now both are 6x.
The same terms.
= 6x = 6x
So yes: they are equivalent.
= yes: equivalent
3 Check
Let's check with a number: x = 2.
The first gives 12.
The second gives 12.
The same.
So the answer is right!
x = 2: 4(2) + 2(2) = 12, 6(2) = 12
Let's look back.
First: group like terms.
Then: compare.
Last: check.
Answer
= yes: equivalent