Question #00584

2 Answers
May 25, 2017

r=E/I-R or r=(E-IR)/I

Explanation:

We want to isolate the r to be by itself.

First let's get rid of the coefficient affecting r. We do this by dividing each side by I.

E/I = (I(R+r))/I
E/I = R+r

Now we want to get r by itself, so we need to move the R somehow. We do this by subtracting R from both sides.

E/I-R = R+r-R
E/I-R=r

That's our answer, but in order to get it in the form of answer c we have to multiply the R by I/I which is technically 1, hence why it works.

E/I-R(I/I)=r
(E-IR)/I=r

Hope that helps!

May 25, 2017

See a solution process below:

Explanation:

First, divide each side of the equation by color(red)(I) to eliminate the need for parenthesis while keeping the equation balanced:

E/color(red)(I) = (I(R + r))/color(red)(I)

E/I = (color(red)(cancel(color(black)(I)))(R + r))/cancel(color(red)(I))

E/I = R + r

Next, subtract color(red)(R) from each side of the equation to solve for r while keeping the equation balanced:

E/I - color(red)(R) = R + r - color(red)(R)

E/I - R = R - color(red)(R) + r

E/I - R = 0 + r

E/I - R = r

r = E/I - R

Answer b is not an option. The other three answers have the solution for r as a fraction over R. Therefore, we need to get the R term over a common denominator:

r = E/I - (I/I xx R)

r = E/I - (IR)/I

r = (E - IR)/I