Final answer:
To solve the equation P = -aw + 9 for w, add aw to both sides, then subtract P from both sides, and finally divide by a to get w = (9 - P) / a. This assumes that a is not zero.
Step-by-step explanation:
The equation provided is P = -aw + 9, and we are to solve for w. This is a basic algebraic task involving isolating the variable of interest, w, to one side of the equation.
Firstly, we'll start by adding aw to both sides of the equation to get rid of the negative sign that is associated with w:
P + aw = 9
Now, we have P + aw = 9 where P is now on the same side as w. Next, we need to group the variable w by itself. So, we subtract P from both sides of the equation, which leaves us with:
aw = 9 - P
Finally, we divide both sides by a to solve for w:
w = (9 - P) / a
Thus, we have expressed w in terms of P and a. It is important to note that in situations like this, we assume that a is not zero because division by zero is undefinable.