Question

Which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number and four”?

(1 – n) – 3 = 1/2(4 – 3n)
3 – (1 – n) = 1/2(4 – 3n)
(n – 1) – 3 = 1/2(3n – 4)
3 – (n – 1) = 1/2(3n – 4)

Answer 1

`3-(n-1)=(1)/(2)(3n-4)`

Explanation:

"three minus the difference of a number and one" this phrase can be written in mathematical form as, 3-(n-1)

and

"one-half of the difference of three times the same number and four" this phrase is written in mathematical form as
`3-(n-1)=(1)/(2)(3n-4)`

according to given statement when above both phrases equals then it is written as mention bellow;

`3-(n-1)=(1)/(2)(3n-4)`

Hence the last provided expression is correct.

Answer 2

The last option is the correct option.
`3-(n-1)=(1)/(2)(3n-4)`

Explanation:

Given statement is: "three minus the difference of a number and one equals one-half of the difference of three times the same number and four”

If the number is
`n` , then "the difference of a number and one" means
`(n-1)`

Now "three minus the difference of a number and one" means
`3-(n-1)`

"The difference of three times the same number and four" means
`(3n-4)` and then "one-half of it" means
`(1)/(2)(3n-4)`

Thus, the expression will be:
`3-(n-1)=(1)/(2)(3n-4)`