Question

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set.

${(x+3)}^2(x+1)>0$

Short answer

The solution set is $(-1,\infty )$

Step-by-step solution

Step 1. Finding the interval.

Given inequality is ${(x+3)}^2(x+1)>0$

The factors on the left-hand side are ${(x+3)}^2,(x+1)$. These factors are zero

When $x=3,-1$.

So, the numbers$-3,-1$ divide the real line into three intervals $(-\infty ,-3),(-3,-1),(-1,\infty )$

Step 2. Determining the sign of each factor.

To determine the sign of each factor on each of the intervals that we found, we use test values. We choose a number inside each intervals and check the sign of each factor.

Step 3. Making the table.

So, the solution set is $(-1,\infty )$

Step 4. Plotting the graph.

Graph or the inequality is