Question

Heyo, help a person out? :)

Answer 1

n =
`(1)/(3)`

Explanation:

for the equation to be true for all values of x , then both sides have to be the same.

expand both sides and equate like terms

left side

12(3n -
`(1)/(2)` x) ← distribute each term in the parenthesis by 12

= 36n - 6x

right side

-
`(2)/(3)` (9x - 18) ← distribute each term in the parenthesis by -
`(2)/(3)`

= - 6x + 12

we require

36n - 6x = - 6x + 12

that is

36n = 12 ( divide both sides by 36 )

n =
`(12)/(36)` =
`(1)/(3)`

for the equation to be true for all x then n =
`(1)/(3)`