If {X/2 - X/6} is an integer, show why X must be a multiple of 3.?

Question

of course the brackets can be read like this:
{X over 2 minus X over 6}

Answer 1

Let n be an integer

Given:
n = x/2 - x/6
n = 3x/6 - x/6
n = (3x - x)/6
n = 2x/6
n = x/3
x = 3n

Because x is 3 times an integer, that is another way of saying it is a multiple of 3.

Answer 2

x/2 - x/6 = integer (= Int)

3x/6 - x/6 = Int

(3x-x)/6 = Int

2x/6 = Int

x/3 = Int

Therefore, x must be divisible by 3. This is because the only solutions are 0, 3, 6, etc. (also -3, -6, etc)

Answer 3

Let "Int" be an integer
(x/2)-(x/6)=Int --- First get a common denominator
(3x/6)-(x/6)= Int ---Then subtract since common denominator
(3x-x)/6 = (2x)/6= Int --- Now reduce fraction
(2/6)x = x/3 = Int ---Now multiply both sides by 3

(x/3) * 3 = Int * 3 so x = 3*Int ---just want you want to prove!!

Answer 4

x/2 - x/6
=
3x/6 - x/6
=
2x/6
=
x/3

Barjesse37

Answer 5

it has to be an even miltiple of 6 because it has to be both divisible by 2 and by 6