The problem describes a rectangle with length $3n+2$ and width $n-1$. The perimeter of the rectangle is given as 42 inches. We need to find the value of $n$.

1. Problem Description

The problem describes a rectangle with length $3n+2$ and width $n-1$. The perimeter of the rectangle is given as 42 inches. We need to find the value of $n$.

2. Solution Steps

The formula for the perimeter $P$ of a rectangle with length $l$ and width $w$ is:

$P = 2l + 2w$

In this case, the length is $l = 3n + 2$ and the width is $w = n - 1$. The perimeter is given as $P = 42$ inches.

Substitute the given values into the perimeter formula:

$42 = 2(3n+2) + 2(n-1)$

Expand the equation:

$42 = 6n + 4 + 2n - 2$

Combine like terms:

$42 = 8n + 2$

Subtract 2 from both sides:

$40 = 8n$

Divide both sides by 8:

$n = \frac{40}{8}$

$n = 5$

3. Final Answer

$n = 5$