Step by step
The question
Question: are 6 + 2x and 8x equivalent?
6 + 2x and 8x
Equivalent means: the two are equal, whatever number the letter is.
equivalent = equal for every number
1 Group like terms
Like terms go together.
6 + 2x is 2x + 6.
= 2x + 6
2 Compare
2x + 6 and 8x are not the same.
= 2x + 6 ≠ 8x
Careful!
A number and an x term are not like terms.
They cannot be added together.
Careful: not 6 + 2x = 8x ✗
So no: they are not equivalent.
= no: not equivalent
3 Check
Let's check with a number: x = 2.
The first gives 10.
The second gives 16.
Different.
So the answer is right!
x = 2: 6 + 2(2) = 10, 8(2) = 16
Let's look back.
First: group like terms.
Then: compare.
Last: check.
Answer
= no: not equivalent