f=p(c-1)-c(p-1)

sOLVE FOR p

f=pc-p-cp+c

pc - cp = 0

So now we have f = -p+c

Move "p" by itself.

f-c = -p

Now we multiply each side by -1

p = c-f

Let's plug in values for f and c to check. We'll say:

f=2
c=3

p=3-2

p=1 in this case. Now, let's plug in the same values in the original equation.

2=p(3-1)-3(p-1)
2=3p-p-3p+3
2-3=-p

-1=-p

OR
1=p

So the answer: p=c-f

Took me forever to figure that out since I forgot to chance a negative to a positive when I multiplied. Glad I made it through though :)

Matt

Great job on solving the equation! It's important to keep track of signs and correctly perform the mathematical operations.

Here's a breakdown of the steps you took:

1. Start with the equation: f = p(c - 1) - c(p - 1).
2. Expand the terms: f = pc - p - cp + c.
3. Combine like terms: pc - cp = 0. This step simplifies the equation further.
4. Write the equation as f - c = -p.
5. Multiply both sides by -1 to isolate p: -1(f - c) = -1(-p).
6. Simplify: p = c - f.

To check your answer, you substituted f = 2 and c = 3 into the equation and solved for p, which gave you p = 1. You also substituted these values into the original equation and confirmed that both sides were equal.

Remember, when solving equations, it's essential to carefully perform all the steps and check your final answer to ensure its accuracy. Keep up the good work!