Question

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

Explanation:

Step1: Simplify both sides

Left side: $\frac{1}{2}(n - 4)-3=\frac{1}{2}n-2 - 3=\frac{1}{2}n-5$
Right side: $3-(2n + 3)=3-2n-3=-2n$

Step2: Solve for n

Set $\frac{1}{2}n-5=-2n$
Add $2n$ to both sides: $\frac{1}{2}n + 2n-5=-2n + 2n$
$\frac{5}{2}n-5 = 0$
Add 5 to both sides: $\frac{5}{2}n=5$
Multiply both sides by $\frac{2}{5}$: $n = 5\times\frac{2}{5}=2$

Answer:

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