Step by step
The question
Question: are 7y − 3y and 4y equivalent?
7y − 3y and 4y
Equivalent means: the two are equal, whatever number the letter is.
equivalent = equal for every number
First we simplify the first one: 7y − 3y.
We write it shorter, with the same value.
= 7y − 3y
1 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the y terms go together.
Each colour is one kind.
like terms = same letters,
same powers
7y − 3y is 4y.
It is like 7 apples take away 3 apples: that is 4 apples.
7y − 3y = 4y
So the expression is 4y.
= 4y
2 Compare
Now both are 4y.
The same terms.
= 4y = 4y
So yes: they are equivalent.
= yes: equivalent
3 Check
Let's check with a number: y = 2.
The first gives 8.
The second gives 8.
The same.
So the answer is right!
y = 2: 7(2) − 3(2) = 8, 4(2) = 8
Let's look back.
First: group like terms.
Then: compare.
Last: check.
Answer
= yes: equivalent