Question

How do you solve for R in `i= (N-P)/( Q-R)`?

Answer 1

Use the rule `a/b = m/n -> b xx m = n xx a`

Explanation:

`i(Q - R) = N - P`

`Q - R = (N - P)/i`

`-R = (N - P)/i - Q`

`R = - (N - P)/i + Q`

Hopefully this helps!

Answer 2

`R = (-N+P+iQ)/i`

Explanation:

The strategy is to get `R` out of the denominator using multiplication, then isolate all terms including `R`, then factor `R` out if necessary, and finally divide by the coefficient of `R`.

`i = (N-P)/(Q-R)`

Multiply each side by `Q-R`.

`=> i(Q-R) = (N-P)/(Q-R)(Q-R) = N-P`

Apply the distributive property to the left hand side.

`=> iQ - iR = N-P`

Subtract `iQ` from each side.

`=> iQ - iR - iQ = N-P-iQ`

`=> -iR = N-P-iQ`

Divide each side by `-i`

`=> (-iR)/(-i) = (N-P-iQ)/(-i)`

`=> R = -(N-P-iQ)/i = (-N+P+iQ)/i`

Answer 3

`R = (P-N)/i + Q` or `R = Q - (N-P)/i`

Explanation:

Here is another method. The biggest problem is that `R` is in the denominator. However, there is only one term on each side of the equal sign., so we can simply invert the entire equation

`1/i = (Q - R)/(N - P)`

Multiply by `(N - P) rArr (N-P)/i = Q - R`

Now : EITHER..... Move `R` to the left and the whole of the term on the left to the right, remembering to change the signs.

`R = Q - (N-P)/i`

OR: Move the Q to the left and then multiply through by -1 to make
-R into +R

`(N-P)/i = Q - R`
`(N-P)/i - Q = - R`

`(P-N)/i + Q = R`