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\?

$3 - (1 - n) = \frac{1}{2}(4 - 3n)$

$3 - (n - 1) = \frac{1}{2}(3n - 4)$

$(n - 1) - 3 = \frac{1}{2}(3n - 4)$

$(1 - n) - 3 = \frac{1}{2}(4 - 3n)$

Explanation:

Step1: Define the number

Let the number be \( n \).

Step2: Translate "the difference of a number and one"

The difference of a number \( n \) and one is \( n - 1 \).

Step3: Translate "three minus the difference of a number and one"

Three minus the difference of a number and one is \( 3 - (n - 1) \).

Step4: Translate "three times the same number"

Three times the same number \( n \) is \( 3n \).

Step5: Translate "the difference of three times the same number and four"

The difference of three times the same number and four is \( 3n - 4 \).

Step6: Translate "one - half of the difference of three times the same number and four"

One - half of the difference of three times the same number and four is \( \frac{1}{2}(3n - 4) \).

Step7: Combine the two parts to form the equation

Combining the two parts, we get the equation \( 3-(n - 1)=\frac{1}{2}(3n - 4) \).

Answer:

\( 3-(n - 1)=\frac{1}{2}(3n - 4) \) (the second option)