We note first that division by zero is not allowed and that for this reason \(9x+9\) may not be equal to zero and that therefore \(x=-1\) is not a solution.

We now distinguish two cases, namely \(9x+9>0\) and \(9x+9<0\).
In both cases we multiply the inequality on both sides by \(9x+9\) because we then get a linear inequality, for which we know there is a solution method.

Suppose \(9x+9>0\), i.e. \(x> -1\). Then we get \(5<-(9x+9)\).
When we move everything with \(x\) to the left and all constant terms to the right, we get \(9x<-14\).
Then, dvision by the coefficient of \(x\)gives \(x < -{{14}\over{9}}\).
So we have the following system of inequalities: \(x> -1\,\wedge\; x < -{{14}\over{9}}\)
and this simplifies to \(\text{an empty solution set}\).

Suppose \(9x+9<0\), i.e. \(x< -1\). Then we get \(5>-(9x+9)\).
When we move everything with \(x\) to the left and all constant terms to the right, we get \(9x>-14\).
Then, division by the coefficient of \(x\) gives \(x > -{{14}\over{9}}\).
So we have the following system of inequalities: \(x< -1\,\wedge\; x > -{{14}\over{9}}\)
and this simplifies to \(-{{14}\over{9}}\lt x\lt -1\).

The solution of the original inequality is \(-{{14}\over{9}}\lt x\lt -1\).