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

Explanation:

Step1: Expand both sides

Expand $\frac{1}{2}(n - 4)-3$ to $\frac{1}{2}n-2 - 3=\frac{1}{2}n-5$, and expand $3-(2n + 3)$ to $3-2n-3=-2n$. So the equation becomes $\frac{1}{2}n-5=-2n$.

Step2: Add $2n$ to both sides

$\frac{1}{2}n+2n-5=-2n + 2n$. Combine like - terms: $\frac{1}{2}n+\frac{4}{2}n-5 = 0$, which simplifies to $\frac{5}{2}n-5 = 0$.

Step3: Add 5 to both sides

$\frac{5}{2}n-5 + 5=0 + 5$, getting $\frac{5}{2}n=5$.

Step4: Multiply both sides by $\frac{2}{5}$

$\frac{2}{5}\times\frac{5}{2}n=5\times\frac{2}{5}$. So $n = 2$.

Answer:

$n = 2$