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

Explanation:

Step1: Analyze "three minus the difference of a number and one"

Let the number be \( n \). The difference of the number and one is \( n - 1 \). Then "three minus this difference" is \( 3-(n - 1) \).

Step2: Analyze "one - half of the difference of three times the same number and four"

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

Step3: Form the equation

Putting the two parts together, the equation is \( 3-(n - 1)=\frac{1}{2}(3n - 4) \).

Answer:

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