To solve the equation [tex]\( p \cdot x + 17 = 12 \)[/tex] for [tex]\( x \)[/tex], follow these steps:
1. Isolate the term involving [tex]\( x \)[/tex]:
Start by subtracting 17 from both sides of the equation:
[tex]\[
p \cdot x + 17 - 17 = 12 - 17
\][/tex]
Simplify the equation:
[tex]\[
p \cdot x = 12 - 17
\][/tex]
[tex]\[
p \cdot x = -5
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
Next, divide both sides of the equation by [tex]\( p \)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-5}{p}
\][/tex]
So, the solution to the equation [tex]\( p \cdot x + 17 = 12 \)[/tex] for [tex]\( x \)[/tex] is [tex]\( x = \frac{-5}{p} \)[/tex].
This corresponds to option D:
[tex]\[
\boxed{x = -\frac{5}{p}}
\][/tex]
