Question

what is the value of n in the equation \\(\frac{1}{2}(n - 4) - 3 = 3 - (2n + 3)\\)?
\\(\bigcirc\\) \\(n = 0\\)
\\(\bigcirc\\) \\(n = 2\\)
\\(\bigcirc\\) \\(n = 4\\)
\\(\bigcirc\\) \\(n = 6\\)

Explanation:

Step1: Simplify both sides

First, simplify the left - hand side: $\frac{1}{2}(n - 4)-3=\frac{1}{2}n-2 - 3=\frac{1}{2}n-5$.
Then, simplify the right - hand side: $3-(2n + 3)=3-2n-3=-2n$.
Now the equation becomes $\frac{1}{2}n-5=-2n$.

Step2: Move terms with n to one side

Add $2n$ to both sides of the equation: $\frac{1}{2}n+2n-5=-2n + 2n$.
We know that $\frac{1}{2}n+2n=\frac{1 + 4}{2}n=\frac{5}{2}n$, so the equation is $\frac{5}{2}n-5 = 0$.

Step3: Solve for n

Add 5 to both sides: $\frac{5}{2}n-5 + 5=0 + 5$, which gives $\frac{5}{2}n=5$.
Multiply both sides by $\frac{2}{5}$: $n = 5\times\frac{2}{5}=2$.

Answer:

B. $n = 2$