Question

solve for n.
n + 1 = 4(n - 8)
options: n = 8, n = 11, n = 16, n = 1

Explanation:

Step1: Expand the right side

Using the distributive property \(a(b - c)=ab - ac\), we expand \(4(n - 8)\) to get \(4n-32\). So the equation becomes \(n + 1=4n-32\).

Step2: Move variable terms to one side

Subtract \(n\) from both sides: \(n + 1 - n=4n-32 - n\), which simplifies to \(1 = 3n-32\).

Step3: Solve for n

Add 32 to both sides: \(1+32 = 3n-32 + 32\), so \(33 = 3n\). Then divide both sides by 3: \(\frac{33}{3}=\frac{3n}{3}\), which gives \(n = 11\).

Answer:

n = 11