Solve the given nonlinear inequality. Write the solution set using interval notation. Graph the solution set.$\frac{5}{x+8}<0$

Key Concepts: Nonlinear Inequality, Interval Notation, Graphing Explanation: To solve the given inequality, we start by finding the critical points. In this case, there is one critical point where $x+8=0$, which is $x=-8$. Next, we can perform a sign test to determine the intervals where the inequality is true. We do this by selecting a test value in each interval. For example, if we choose $x=-10$, we get:\n $\frac{5}{-10+8}=-\frac{5}{2}<0$\n which means the inequality is true in the interval $x\in (-\infty ,-8)$. If we choose $x=-7$, we get:\n $\frac{5}{-7+8}=5>0$\n which means the inequality is false in the interval $x\in (-8,\infty )$. Therefore, the solution set is $(-\infty ,-8)$. Graphically, this represents all points to the left of $x=-8$ on the number line. Step by Step Solution: Step 1. Find the critical point(s) by setting the numerator and denominator equal to zero: Step 2. Perform a sign test on each interval to determine where the inequality is true. Step 3. Write the solution set using interval notation. Step 4. Graph the solution set on the number line. Final Answer: $(-\infty ,-8)$