We note first that division by zero is not allowed and that for this reason \(4x+4\) may not be equal to zero and that therefore \(x=-1\) is not a solution.

We now distinguish two cases, namely \(4x+4>0\) and \(4x+4<0\).
In both cases we multiply the inequality on both sides by \(4x+4\) because we then get a linear inequality, for which we know there is a solution method.

Suppose \(4x+4>0\), i.e. \(x> -1\). Then we get \(8<-(4x+4)\).
When we move everything with \(x\) to the left and all constant terms to the right, we get \(4x<-12\).
Then, dvision by the coefficient of \(x\)gives \(x < -3\).
So we have the following system of inequalities: \(x> -1\,\wedge\; x < -3\)
and this simplifies to \(\text{an empty solution set}\).

Suppose \(4x+4<0\), i.e. \(x< -1\). Then we get \(8>-(4x+4)\).
When we move everything with \(x\) to the left and all constant terms to the right, we get \(4x>-12\).
Then, division by the coefficient of \(x\) gives \(x > -3\).
So we have the following system of inequalities: \(x< -1\,\wedge\; x > -3\)
and this simplifies to \(-3\lt x\lt -1\).

The solution of the original inequality is \(-3\lt x\lt -1\).