How to solve Lotka-Volterra with periodic coefficients differential inequality

Question

I would like to ask which transformation should I use to recive from this Lotka-Volterra inequality $$x'=x(a-bx-cy)<x(a-bx)$$ this differential form $$x(t)\leq \frac{x(T)e^{A(t)}}{1+x(T)\int_{T}^{t}e^{A(s)}b(s)ds}, \text{where} A(t)=\int_{T}^{t}a(s)ds.$$

Answer 1

Divide by $x^2$ to get a linear differential inequality $$ -(x^{-1})'\le ax^{-1}-b, $$ Apply the integrating factor $e^{A(t)}$ where $A'(t)=a(t)$ $$ be^{A(t)}\le (e^{A(t)}x^{-1})' $$ integrate on both sides over $[T,t]$, then solve for $x(t)$.