Question

which expression are equivalent to 3(n+4)? Select each correct answer. 12+n+n+n, 3n+4, 3n-12, 2n+12+n.

Answer 1

12+n+n+n 2n+12+n Let's look at each option and see if they can be manipulated into 3(n+4). 12+n+n+n * TRUE. This can be changed into 12 + 3n and then the 3 can be factored out to get 3(4 + n). Finally, due to the commutative property of addition, we can swap the 4 and n to get 3(n+4). 3n+4 * FALSE. It looks like someone attempted to distribute the 3 in 3(n+4) and forgot to continue the distribution to the 4. So this is wrong. 3n-12 * FALSE. There's no negative term anywhere in 3(n+4), so that minus 12 doesn't make any sense. 2n+12+n * TRUE. Combine the 2n and n terms to get 3n, so you now have 3n+12. Factor out the 3 and you get 3(n+4) and therefore this works.