Step by step
The question
Question: are 2(3a + 1) and 6a + 1 equivalent?
2(3a + 1) and 6a + 1
Equivalent means: the two are equal, whatever number the letter is.
equivalent = equal for every number
First we simplify the first one: 2(3a + 1).
We write it shorter, with the same value.
= 2(3a + 1)
1 Open the brackets
The 2 in front of the bracket multiplies every part inside.
a(b + c) = ab + ac
So we write 2 times each part.
= 2(3a) + 2(1)
2 times 3a is 6a.
2 times 1 is 2.
= 6a + 2
2 Compare
6a + 2 and 6a + 1 are not the same.
= 6a + 2 ≠ 6a + 1
So no: they are not equivalent.
= no: not equivalent
3 Check
Let's check with a number: a = 2.
The first gives 14.
The second gives 13.
Different.
So the answer is right!
a = 2: 2(3(2) + 1) = 14, 6(2) + 1 = 13
Let's look back.
First: open the brackets.
Then: compare.
Last: check.
Answer
= no: not equivalent