Let's start with the given equation and try to isolate [tex]\( h \)[/tex]. The given equation is:
[tex]\[ P = \frac{h + v}{3} \][/tex]
The goal is to solve for [tex]\( h \)[/tex] in terms of [tex]\( P \)[/tex] and [tex]\( v \)[/tex].
1. Eliminate the fraction: Multiply both sides of the equation by 3 to get rid of the denominator:
[tex]\[ 3P = h + v \][/tex]
2. Isolate [tex]\( h \)[/tex]: To solve for [tex]\( h \)[/tex], subtract [tex]\( v \)[/tex] from both sides of the equation:
[tex]\[ h = 3P - v \][/tex]
Therefore, the equivalent form of the equation is:
[tex]\[ h = 3P - v \][/tex]
To identify the correct answer from the provided options:
- A: [tex]\( h = \frac{P - v}{3} \)[/tex]
- B: [tex]\( h = 3(P - v) \)[/tex]
- C: [tex]\( h = \frac{P}{3} - v \)[/tex]
- D: [tex]\( h = 3P - v \)[/tex]
The correct equivalent form is:
[tex]\[ D: \quad h = 3P - v \][/tex]
So the answer is [tex]\( \boxed{4} \)[/tex].
