If I had the old-fashion camera that had a focal length of 35mm(0.035m) and I take a picture of a person 6 m away, how far does the film need to be from the lens to record a clear image?

I know that the equation is 1/f = 1/d(object) + 1/d(image) so would I do the following:
1/0.035m = 1/6 +1/unknown and then solve, yes or no?

Yes, you are on the right track in using the lens formula to solve this problem. The lens formula, 1/f = 1/d(object) + 1/d(image), relates the focal length of a lens (f) to the distances of the object (d(object)) and image (d(image)) from the lens.

In this case, you know the focal length of the camera lens is 0.035m and the distance of the person (object) from the lens is 6m. You want to find the distance of the film (image) from the lens to record a clear image. Let's denote it as d(film).

So, you can write the equation as:
1/0.035 = 1/6 + 1/d(film)

To solve for d(film), you need to rearrange the equation to isolate it. Multiply through by the common denominator (0.035 * 6 * d(film)) to get rid of the fractions:
(0.035 * 6 * d(film)) / (0.035) = (0.035 * 6 * d(film)) / 6 + (0.035 * 6 * d(film)) / d(film)

Simplifying the equation gives:
6 * d(film) = 0.035 * 6 + 0.035 * d(film)

Further simplifying:
6 * d(film) = 0.21 + 0.035 * d(film)

Rearranging the terms:
6 * d(film) - 0.035 * d(film) = 0.21

Combine like terms:
5.965 * d(film) = 0.21

Finally, divide both sides by 5.965 to find d(film):
d(film) = 0.210 / 5.965

Therefore, the film needs to be approximately 0.0352 meters (or 3.52 cm) from the lens to record a clear image.

Note: In this answer, we assumed the units remain consistent throughout the calculation (in this case, meters).