Answer
$(-\infty,-5)\cup(-3,\infty)$
Work Step by Step
Step 1. Rewrite the inequality as $\frac{x+1}{x+3}-2\lt0$, which gives $\frac{x+1-2x-6}{x+3}\lt0$, $\frac{-x-5}{x+3}\lt0$, and $\frac{x+5}{x+3}\gt0$
Thus the boundary points are $x=-5,-3$
Step 2. Using test points to examine signs across the boundary points, we have
$...(+)...(-5)...(-)...(-3)...(+)...$
Thus the solutions are $x\lt-5$ or $ x\gt-3$
Step 3. We can express the solutions on a real number line as shown in the figure.
Step 4. We can express the solutions in interval notation as $(-\infty,-5)\cup(-3,\infty)$