Questions: What is the value of n in the equation 1/2(n-4)-3=3-(2n+3)? n=0 n=2 n=4 n=6

Solution Steps

To solve for $n$ in the equation $\frac{1}{2}(n-4)-3=3-(2n+3)$, we need to follow these steps:

1. Distribute the $\frac{1}{2}$ on the left side.
2. Simplify both sides of the equation.
3. Combine like terms and isolate $n$.

Starting with the equation: $$\frac{1}{2}(n-4) - 3 = 3 - (2n + 3)$$

Distribute $\frac{1}{2}$ on the left side: $$\frac{1}{2}n - 2 - 3 = 3 - 2n - 3$$

Simplify both sides: $$\frac{1}{2}n - 5 = -2n$$

Combine like terms to isolate $n$: $$\frac{1}{2}n + 2n = 5$$

Combine the terms on the left side: $$2.5n = 5$$

Divide both sides by 2.5: $$n = \frac{5}{2.5} = 2$$

Final Answer