Step by step
The question
Question: are 3(2y + 4) and 6y + 7 equivalent?
3(2y + 4) and 6y + 7
Equivalent means: the two are equal, whatever number the letter is.
equivalent = equal for every number
First we simplify the first one: 3(2y + 4).
We write it shorter, with the same value.
= 3(2y + 4)
1 Open the brackets
The 3 in front of the bracket multiplies every part inside.
a(b + c) = ab + ac
So we write 3 times each part.
= 3(2y) + 3(4)
3 times 2y is 6y.
3 times 4 is 12.
= 6y + 12
2 Compare
6y + 12 and 6y + 7 are not the same.
= 6y + 12 ≠ 6y + 7
So no: they are not equivalent.
= no: not equivalent
3 Check
Let's check with a number: y = 2.
The first gives 24.
The second gives 19.
Different.
So the answer is right!
y = 2: 3(2(2) + 4) = 24, 6(2) + 7 = 19
Let's look back.
First: open the brackets.
Then: compare.
Last: check.
Answer
= no: not equivalent