Question

How do you solve for P in `S=B+(1/2)Pl`?

Answer 1

See the entire solution process below:

Explanation:

First, subtract `color(red)(B)` from each side of the equation to isolate the term containing `P` while keeping the equation balanced:

`S - color(red)(B) = -color(red)(B) + B + (1/2)Pl`

`S - B = 0 + (1/2)Pl`

`S - B = (1/2)Pl`

Next, multiply each side of the equation by `color(red)(2)` to eliminate the fraction while keeping the equation balanced:

`color(red)(2)(S - B) = color(red)(2) xx (1/2)Pl`

`2(S - B) = cancel(color(red)(2)) xx (1/color(red)(cancel(color(black)(2))))Pl`

`2(S - B) = Pl`

Now, divide each side of the equation by `color(red)(l)` to solve for `P` while keeping the equation balanced:

`(2(S - B))/color(red)(l) = (Pl)/color(red)(l)`

`(2(S - B))/l = (Pcolor(red)(cancel(color(black)(l))))/cancel(color(red)(l))`

`(2(S - B))/l = P`

`P = (2(S - B))/l`