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: $3-(2n + 3)=3-2n-3=-2n$

Step2: Solve for n

Set the simplified left - hand side equal to the simplified right - hand side:
$\frac{1}{2}n-5=-2n$
Add $2n$ to both sides: $\frac{1}{2}n+2n-5=-2n + 2n$
$\frac{1 + 4}{2}n-5 = 0$ (since $2n=\frac{4}{2}n$)
$\frac{5}{2}n-5 = 0$
Add 5 to both sides: $\frac{5}{2}n-5 + 5=0 + 5$
$\frac{5}{2}n=5$
Multiply both sides by $\frac{2}{5}$: $n = 5\times\frac{2}{5}$
$n = 2$

Answer:

B. $n = 2$