Question

Suppose x is a number such that 2x=x/2-6. Must it then be true that 3x=12. Explain your reasoning

Answer 1

2x = x/2 - 6.....multiply both sides by 2
4x = x - 12
4x - x = -12
3x = -12
x = -12/3
x = -4

3x = 12......3(-4) = 12.....-12 = 12...false......so 3x = 12 is not true because x = -4

Answer 2

2x = x/2 - 6
6 + 2x = x/2
8x = x/2
x^2 = 8/2
x^2 = 4
x^2 - 4 = 0
(x - 2) (x + 2) = 0
x = 2 and x = -2

False

This is the actual right answer :) a teacher saw this :)