College Algebra (6th Edition)

$-6\lt x\lt0$
The absolute value will keep the sign the same and the other side positive, and it will also flip the sign and make the other side negative. Solve for each inequality by multiplying both sides, subtracting from both sides, and dividing. $|\frac{2x+6}{3}|\lt2$ $\frac{2x+6}{3}\lt2$ $2x+6\lt6$ $2x\lt0$ $x\lt0$ $\frac{2x+6}{3}\gt-2$ $2x+6\gt-6$ $2x\gt-12$ $x\gt-6$ $-6\lt x\lt0$