Answer
More than a $32,000\space dollar$ price would make the first bill a better deal for the homeowner.
Work Step by Step
Let the price range of home assessment be $x$.
The first bill price is $\$1800$ plus $3\%$ of assessed home value.
The second bill price is $\$200$ plus $8\%$ of assessed home value.
In the mathematical form.
The first bill price $=1800+0.03x$.
The second bill price $=200+0.08x$.
For the first bill to be the better deal the inequality is.
The second bill price $>$ The first bill price.
The inequality is
$\Rightarrow 200+0.08x>1800+0.03x$.
Add $-200-0.03x$ to both sides.
$\Rightarrow 200+0.08x-200-0.03x>1800+0.03x-200-0.03x$.
Simplify.
$\Rightarrow 0.05x>1600$.
Divide both sides by $0.05$.
$\Rightarrow \frac{0.05x}{0.05}>\frac{1600}{0.05}$.
Simplify.
$\Rightarrow x>32,000$.
More than a $32,000\space dollar$ price would make the first bill a better deal for the homeowner.
