Answer
The solution is $(8,9)$
Work Step by Step
$-\dfrac{1}{4}\gt\dfrac{6-x}{12}\gt-\dfrac{1}{6}$
Multiply the whole inequality by $12$:
$12\Big(-\dfrac{1}{4}\gt\dfrac{6-x}{12}\gt-\dfrac{1}{6}\Big)$
$-\dfrac{12}{4}\gt6-x\gt-\dfrac{12}{6}$
$-3\gt6-x\gt-2$
Subtract $6$ from each side:
$-3-6\gt6-6-x\gt-2-6$
$-9\gt-x\gt-8$
Change the sign of all three sides:
$9\gt x\gt8$
Expressing the solution in interval notation:
$(8,9)$
