Final answer:
To solve for z in the equation 16z + 29z = pz - v, we combine like terms, factor z out, and then isolate z resulting in the solution z = -v / (45 - p), assuming p does not equal 45.
Step-by-step explanation:
Given the equation 16z + 29z = pz - v, the task is to solve for z when assuming that the equation has a solution for z. To find z, we first need to combine like terms on the left side of the equation:
45z = pz - v
Now we will isolate z on one side of the equation by moving all terms involving z to one side and other terms to the opposite side:
45z - pz = -v
We can factor z out from the left side:
z(45 - p) = -v
To solve for z, we divide both sides by (45 - p), assuming that p does not equal 45 to avoid division by zero:
z = -v / (45 - p)
This represents the value of z in terms of v and p.