Maths question help please differential equation

Hi, please could I have some help on the question below. I’m not sure how 100-P became 0P-100?
Question: https://ibb.co/ZzKvWSk4
Thanks!

Thinking about he original ode, theres a divide by zero when P(t) = 100 (horizontal line on P-t graph so you might expect theres a problem with this.
But working down, you have
|100-P| = 1900e^(-t)
so there are two possible solutions on the left so +(100-P) and -(100-P). The initial condition says P(0) = 2000 which can only be satisfied by the second expression, otherwise, for the first, youd have at t=0
100-2000 = 1900
The second one gives 1900 = 1900
Plotting the curve(s) in desmos give
https://www.desmos.com/calculator/0ra1sjqrcm
only one satisfies the initial condition and both have a horizontal asymptote at P=100

Hi, please could I have some help on the question below. I’m not sure how 100-P became 0P-100?
Question: https://ibb.co/ZzKvWSk4
Thanks!

It's a miscommunication - both methods converge to the same answer. It's just that the method on the left has on extra step while the method on the right is blank during that step. Makes it look like it disappears.

Using either "method", left of right, (theyre basically the same) you have to reason about removing the absolute value function and determine which of the solutions satisfies the initial condition. Theres no miscommunication.