Sure, let's solve the given proportion step-by-step:
The proportion given is:
[tex]\[
\frac{p-5}{p+1} = \frac{2}{3}
\][/tex]
To solve for [tex]\( p \)[/tex], we will use cross-multiplication. Cross-multiplication involves multiplying each side of the equation by the denominators of the other side. This gives us:
[tex]\[
3(p-5) = 2(p+1)
\][/tex]
Next, distribute the numbers on both sides:
[tex]\[
3p - 15 = 2p + 2
\][/tex]
Now, we need to get all the terms containing [tex]\( p \)[/tex] on one side and the constant terms on the other side. Subtract [tex]\( 2p \)[/tex] from both sides:
[tex]\[
3p - 2p - 15 = 2
\][/tex]
[tex]\[
p - 15 = 2
\][/tex]
To isolate [tex]\( p \)[/tex], add 15 to both sides of the equation:
[tex]\[
p = 2 + 15
\][/tex]
[tex]\[
p = 17
\][/tex]
So, the solution to the equation is:
[tex]\[
p = 17
\][/tex]
Thus, from the given options, the correct value for [tex]\( p \)[/tex] is:
[tex]\[
\boxed{17}
\][/tex]
