3(-n + 4) + 5n = 2n A) n = 3 B) no solution C) infinitely many solutions

B

Step-by-step explanation:

Given

3(- n + 4) + 5n = 2n ← distribute and simplify left side

- 3n + 12 + 5n = 2n

2n + 12 = 2n ( subtract 12 from both sides )

2n = 2n - 12 ( subtract 2n from both sides )

0 = - 12 ← not possible

This indicates the equation has no solution

Comparing the types of solutions

A n = 3

Indicates that there is only one unique solution to the equation.

B no solutions

This is indicated when you solve and obtain a ridiculous statement, similar to the one obtained in part A, that is

0 = 12

C infinite solutions

This is indicated when you solve the equation and obtain

4 = 4 or - 3 = - 3