Hello Louis!
In order to tackle these problems one must remember what each of the variables mean. Then, we can rearrange the equation as needed to solve for the unknown variable.
p(x) : This is a function, where x is your inputs and p(x) is your outputs. In essence, p(x) can be thought of as another number. Here, p(x) is the price per gallon.
x : This is simply the "wholesale price of gas" as stated above.
Now, in order to rearrange the equation, we need to identify what we are solving for. Because we are solving for wholesale price, we are solving for x. We need to rearrange the equation above to isolate x on one side, and everything else on the other. Why? So we can find the value of x!
p(x) = 0.46 + 0.9x (original)
p(x) - 0.46 = 0.9x (move the constant to the other side by subtracting 0.46 from both sides)
[ p(x) - 0.46] / 0.9 = x (isolate x by dividing by 0.9 on both sides)
There you have it! All that is left to do is to plug in the value for p(x) to solve for x:
p(x) = price per gallon = 3.63
[ p(x) - 0.46] / 0.9 = x
[3.63 - 0.46] / 0.9 = x = 3.52
Remember your units! x = $3.52, which is the wholesale price of gas given that the station is charging $3.63 per gallon.
