Let's solve the given equation step-by-step.
We start with the equation:
[tex]\[ 3p - 7 + p = 13 \][/tex]
Step 1: Combine the like terms on the left side of the equation. The like terms here are [tex]\(3p\)[/tex] and [tex]\(p\)[/tex].
[tex]\[ 3p + p - 7 = 13 \][/tex]
[tex]\[ 4p - 7 = 13 \][/tex]
So, the resulting equation after the first step in the solution is:
[tex]\[ 4p - 7 = 13 \][/tex]
Thus, the correct answer is:
[tex]\[ 4p - 7 = 13 \][/tex]