Let's take a detailed, step-by-step approach to solve the equation and determine the correct answer:
1. Given Equation:
[tex]\[ 3p - 7 + p = 13 \][/tex]
2. Combine Like Terms:
Combine the [tex]\( p \)[/tex] terms on the left side.
[tex]\[ 3p + p - 7 = 13 \][/tex]
Simplify by adding the coefficients of [tex]\( p \)[/tex]:
[tex]\[ 4p - 7 = 13 \][/tex]
3. Isolate [tex]\( 4p \)[/tex]:
To get [tex]\( 4p \)[/tex] by itself, move the constant term [tex]\(-7\)[/tex] to the right side of the equation.
Add [tex]\( 7 \)[/tex] to both sides:
[tex]\[ 4p - 7 + 7 = 13 + 7 \][/tex]
This simplifies to:
[tex]\[ 4p = 20 \][/tex]
The initial step to isolate [tex]\( 4p \)[/tex] was done here:
When the constants are moved and terms are simplified, one of the intermediate steps would be noticing that the equation transformed and simplified, as shown here:
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]
