The Goal

Solve the following inequality for n (assumed to be positive):

The Mistake

Find the algebra mistake:

Need a hint? Look carefully at the red part of the algebra:

The Correction

An Explanation

There are two issues. First, when the reciprocal is taken the inequality reverses. Second, the reciprocal of 10^-6 is 10⁶, since 10^-6 is 1/10⁶.