Answer
$r=-6$
Work Step by Step
$$\begin{align*}
5(r)+5(9)-2(1)-2(-r)&=1 &\text{Apply the Distributive Property}\\
5r+45-2+2r&=1 &\text{Simplify.}\\
7r+43&=1 &\text{Combine like terms.}\\
7r+43-43&=1-43 &\text{Subtract 43 from each side.}\\
7r&=-42 &\text{Simplify.}\\
\frac{7r}{7}&=\frac{-42}{7} &\text{Divide 7 to both sides.}\\
r&=-6&\text{Simplify.}
\end{align*}$$
Check the answer by substituting $-6$ to the variable in the given equation.
$$\begin{align*}
5(r+9)-2(1-r)&=1\\
5(-6+9)-2[1-(-6)]&\stackrel{?}{=}1\\
15-14&\stackrel{?}{=}1\\
1&\stackrel{\checkmark}{=}1
\end{align*}$$
Thus, the solution is $r=-6$.
