I=2V/R+2r

Solve for r.

Subtract 2V/R from both sides, then divide by 2.

(I-2V/R)/2 = r

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To solve for r in the equation I = 2V/R + 2r, we will isolate the term containing r on one side of the equation.

Let's start by subtracting 2r from both sides to move it to the left side:

I - 2r = 2V/R

Now, let's isolate r by dividing the entire equation by 2:

(I - 2r) / 2 = (2V/R) / 2

Simplifying both sides:

(I - 2r) / 2 = V/R

Next, let's multiply both sides of the equation by R to cancel out the denominator on the right side:

R * (I - 2r) / 2 = V

Expanding the left side:

(R * I - 2R * r) / 2 = V

Now, let's multiply both sides of the equation by 2 to eliminate the denominator:

2 * (R * I - 2R * r) / 2 = 2 * V

Simplifying:

R * I - 2R * r = 2V

Finally, let's isolate the term containing r by moving the other terms to the right side:

- 2R * r = 2V - R * I

Dividing both sides by -2R, we get:

r = (2V - R * I) / -2R

So, the solution for r in the equation I = 2V/R + 2r is r = (2V - R * I) / -2R.