Us to solve the equation 3sqrt(4x−3) − sqrt(5x+1) = 3 where x is an integer.

The problem asks us to solve the equation $3\sqrt{4x-3} - \sqrt{5x+1} = 3$ where $x$ is an integer.

Step 1: Determine the domain of the variables.
For the square roots to be defined, the expressions under them must be non-negative:
$4x-3 \ge 0 \implies 4x \ge 3 \implies x \ge \frac{3}{4}$
$5x+1 \ge 0 \implies 5x \ge -1 \implies x \ge -\frac{1}{5}$
Combining these, we must have $x \ge \frac{3