Substitute \(x=-\frac{1}{34}\) into \(px=3x+1\).
Start with the original equation.
\[px=3x+1\]
Let \(x=-\frac{1}{34}\).
\[p\times \frac{-1}{34}=3\times \frac{-1}{34}+1\]
Simplify.
\[-\frac{p}{34}=\frac{31}{34}\]
\[-\frac{p}{34}=\frac{31}{34}\]
Solve for \(p\) in \(-\frac{p}{34}=\frac{31}{34}\).
Solve for \(p\).
\[-\frac{p}{34}=\frac{31}{34}\]
Multiply both sides by \(34\).
\[-p=\frac{31}{34}\times 34\]
Cancel \(34\).
\[-p=31\]
Multiply both sides by \(-1\).
\[p=-31\]
\[p=-31\]
Therefore,
\[\begin{aligned}&p=-31\\&x=-\frac{1}{34}\end{aligned}\]
p=-31;x=-1/34
