## Intermediate Algebra (6th Edition)

The solution is $(8,9)$
$-\dfrac{1}{4}\gt\dfrac{6-x}{12}\gt-\dfrac{1}{6}$ 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: $(8,9)$