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To begin, we can write an expression to determine the cost spent at each campground. Let $x$ be the number of nights we camp. At Calverton River Campgrounds they charge a fee of $\$85$ and $\$40$ per night.
$\begin{gathered}
85+40x
\end{gathered}$
At Shawnee Lake Campgrounds they charge a fee of $\$25$ and $\$52$ per night.
$\begin{gathered}
25+52x
\end{gathered}$
We want to know how many nights, $x,$ we have to stay to make Calverton River Campgrounds cheaper than Shawnee Lake Campgrounds. We find that by solving the inequality $85+40x<25+52x.$
Thus, Calverton River Campgrounds is cheaper for a stay longer than $5$ nights.

$85+40x<25+52x$

SubIneq$\text{LHS}-25<\text{RHS}-25$

$60+40x<52x$

SubIneq$\text{LHS}-40x<\text{RHS}-40x$

$60<12x$

DivIneq$\left.\text{LHS}\middle/12\right.<\left.\text{RHS}\middle/12\right.$

$5<x$

RearrangeIneqRearrange inequality

$x>5$