Question

what is the value of n in the equation $-\frac{1}{2}(2n + 4) + 6 = -9 + 4(2n + 1)$?
n = \boxed{}

Explanation:

Step1: Distribute the terms

First, distribute \(-\frac{1}{2}\) to \(2n + 4\) and \(4\) to \(2n + 1\):
\(-\frac{1}{2}(2n) - \frac{1}{2}(4) + 6 = -9 + 4(2n) + 4(1)\)
Simplify each term:
\(-n - 2 + 6 = -9 + 8n + 4\)

Step2: Combine like terms

Simplify both sides by combining constants:
Left side: \(-n + 4\)
Right side: \(8n - 5\)
Equation becomes: \(-n + 4 = 8n - 5\)

Step3: Isolate the variable

Add \(n\) to both sides: \(4 = 9n - 5\)
Add \(5\) to both sides: \(9 = 9n\)

Step4: Solve for \(n\)

Divide both sides by \(9\): \(n = \frac{9}{9} = 1\)

Answer:

\(n = 1\)