Question

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

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: $3-(2n + 3)=3-2n-3=-2n$.
So the equation becomes $\frac{1}{2}n-5=-2n$.

Step2: Add 2n to both sides

Add $2n$ to both sides of the equation $\frac{1}{2}n-5=-2n$:
$\frac{1}{2}n+2n-5=-2n + 2n$.
$\frac{1 + 4}{2}n-5 = 0$ (since $2n=\frac{4}{2}n$), so $\frac{5}{2}n-5 = 0$.

Step3: Add 5 to both sides

Add 5 to both sides of the equation $\frac{5}{2}n-5 = 0$:
$\frac{5}{2}n-5 + 5=0 + 5$.
$\frac{5}{2}n=5$.

Step4: Solve for n

Multiply both sides of the equation $\frac{5}{2}n=5$ by $\frac{2}{5}$:
$n = 5\times\frac{2}{5}$.
$n = 2$.

Answer:

$n = 2$ (corresponding to the option "n = 2")