Answer
$\color{blue}{(-1 +\infty)}$
Work Step by Step
Find the value/s of $x$ that will make the denominator equal to zero by equating the denominator to zero then solving the equation.
$$x+1=0 \longrightarrow x=-1$$
Solve the related equation:
$$\dfrac{5}{x+1}=0$$
Multiply $x+1$ to both sides of the equation to obtain:
$$\\5=0(x+1)
\\5=0$$
The equation has no solution.
The number $-1$ divides the number line into two regions, namely:
A $(-\infty, -1)$
B $(-1, +\infty)$
Pick a test point value in each region and substitute it into the given inequality. If the test point satisfies the given inequality, then the region where the test point value belongs is a solution. (Refer to the table below.)
Thus, the solution includes the interval $(-1, +\infty)$.
$-1$ is not included because it makes the denominator equal to zero (and the inequality involved is $gt$).
Therefore, the solution is:
$\color{blue}{(-1 +\infty)}$
