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

May 13, 2016

Use the rule $\frac{a}{b} = \frac{m}{n} \to b \times m = n \times a$

#### Explanation:

$i \left(Q - R\right) = N - P$

$Q - R = \frac{N - P}{i}$

$- R = \frac{N - P}{i} - Q$

$R = - \frac{N - P}{i} + Q$

Hopefully this helps!

May 13, 2016

$R = \frac{- N + P + i Q}{i}$

#### 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 $R$.

$i = \frac{N - P}{Q - R}$

Multiply each side by $Q - R$.

$\implies i \left(Q - R\right) = \frac{N - P}{Q - R} \left(Q - R\right) = N - P$

Apply the distributive property to the left hand side.

$\implies i Q - i R = N - P$

Subtract $i Q$ from each side.

$\implies i Q - i R - i Q = N - P - i Q$

$\implies - i R = N - P - i Q$

Divide each side by $- i$

$\implies \frac{- i R}{- i} = \frac{N - P - i Q}{- i}$

$\implies R = - \frac{N - P - i Q}{i} = \frac{- N + P + i Q}{i}$

May 14, 2016

$R = \frac{P - N}{i} + Q$ or $R = Q - \frac{N - P}{i}$

#### 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

$\frac{1}{i} = \frac{Q - R}{N - P}$

Multiply by $\left(N - P\right) \Rightarrow \frac{N - P}{i} = Q - R$

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

$R = Q - \frac{N - P}{i}$

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

$\frac{N - P}{i} = Q - R$
$\frac{N - P}{i} - Q = - R$

$\frac{P - N}{i} + Q = R$