Answer
$(-\displaystyle \infty,-\frac{21}{2})$.
Work Step by Step
$\displaystyle \frac{x}{3}-\frac{3}{4}-1 \gt \frac{x}{2} \qquad ...$ multiply with 12, the LCD.
$4x-9-12 \gt 6x \qquad ...$ add $-4\mathrm{x}$ to both sides, simplify
$-21 \gt 2x\qquad ...$ divide with 2
$-\displaystyle \frac{21}{2} \gt x$
or
$x \lt -\displaystyle \frac{21}{2}$
The solution set is $(-\displaystyle \infty,-\frac{21}{2})$.
