14) -16 + 5n = -7(-6 + 8n) + 3

Explanation:

Step1: Expand the right - hand side

First, expand $-7(-6 + 8n)+3$ using the distributive property $a(b + c)=ab+ac$. So, $-7(-6 + 8n)+3=(-7)\times(-6)+(-7)\times(8n)+3 = 42-56n + 3=45-56n$. The equation becomes $-16 + 5n=45-56n$.

Step2: Add $56n$ to both sides

To get all the $n$ terms on one side, add $56n$ to both sides of the equation: $-16 + 5n+56n=45-56n+56n$. Simplifying gives $-16 + 61n=45$.

Step3: Add 16 to both sides

To isolate the term with $n$, add 16 to both sides: $-16+16 + 61n=45 + 16$. This simplifies to $61n=61$.

Step4: Solve for $n$

Divide both sides by 61: $\frac{61n}{61}=\frac{61}{61}$. So, $n = 1$.

Answer:

$n = 1$