# How do you solve T=(3R)/(M-N)  for R?

Oct 1, 2015

Remember $\frac{a}{b} = \frac{c}{d} \to a d = b c$ (cross-product)

#### Explanation:

$\frac{T}{1} = \frac{3 R}{M - N} \to T \cdot \left(M - N\right) = 1 \cdot 3 R \to$

$3 R = T \left(M - N\right) \to R = \frac{1}{3} T \left(M - N\right) = \frac{T \left(M - N\right)}{3}$

Oct 1, 2015

$R = \frac{T M - T N}{3}$

#### Explanation:

First of you need to multiply both sides by $M - N$;
$T \left(M - N\right) = \frac{3 R}{M - N} \left(M - N\right) = T M - T N = 3 R$
Then you need to divide both sides by three;
$\frac{T M - T N}{3} = \frac{3 R}{3} = \frac{T M - T N}{3} = R$
Hope that helps :)