Solving formulas is much like solving general linear equations. The only difference is we will have several variables in the problem and we will be attempting to solve for one specific variable. For example, we may have a formula such as `A = πr^2 + πrs` (formula for surface area of a right circular cone) and we may be interested in solving for the variable `s`. This means we want to isolate the `s` so the equation has `s` on one side, and everything else on the other. So a solution might look like `s = (A−πr^2)/(πr)`. This second equation gives the same information as the first, they are algebraically equivalent, however, one is solved for the area, while the other is solved for `s` (slant height of the cone). In this section we will discuss how we can move from the first equation to the second. When solving formulas for a variable we need to focus on the one variable we are trying to solve for, all the others are treated just like numbers. This is shown in the following example. Two parallel problems are shown, the first is a normal one- step equation, the second is a formula that we are solving for `x` Example

`3x = 12`	`ax=b`	In both problems, `x` is multiplied by something
`(3x)/color(red)(3) = 12/color(red)(3)`	`(ax)/color(red)(a)=b/color(red)(a)`	To isolate the `x` we divide by `3` or `a`.
`x = 4`	`x = b/a `	Solution

We use the same process to solve `3x=12` for `x` as we use to solve` ax=b` for `x`. Because we are solving for `x` we treat all the other variables the same way we would treat numbers. Thus, to get rid of the multiplication we divided by `a`. This same idea is seen in the following example. Example `m + n = p` for `n`

`m + n = p`	Solving for n, treat all other variables like numbers
`m + ncolor(red)(-n) = pcolor(red)(-n)`	Subtract m from both sides
`m = p-n`	solution

As p and m are not like terms, they cannot be combined. For this reason we leave the expression as p − m. This same one-step process can be used with grouping symbols. Example `a(x−y) = b` for a

`a(x−y) = b`	Solving for `a`,treat `(x−y)` like a number
`(a(x−y))/color(red)((x-y)) = b/color(red)((x-y)) `	Divide both sides by `(x−y)`
`a= b/(x-y) `	Solution

Because `(x − y)` is in parenthesis, if we are not searching for what is inside the parenthesis, we can keep them together as a group and divide by that group. However, if we are searching for what is inside the parenthesis, we will have to break up the parenthesis by distributing. The following example is the same formula, but this time we will solve for `x`. Example `a(x−y)=b` for x

`a(x−y)=b`	Solving for x, we need to distribute to clear parenthesis
`ax−ay=b `	Focus on `ay`
`ax−ay color(red)(+ay)=b color(red)(+ay) `	Add `ay` to both sides
`ax=b+ay`	The `x`is multipied by `a`
`(ax)/color(red)(a)=(b+ay)/color(red)(a)`	Divide both sides by a
`x=(b+ay)/a`	Solution