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