We note first that division by zero is not allowed and that for this reason \(2x+7\) may not be equal to zero and that therefore \(x=-{{7}\over{2}}\) is not a solution.

We now distinguish two cases, namely \(2x+7>0\) and \(2x+7<0\).
In both cases we multiply the inequality on both sides by \(2x+7\) because we then get a linear inequality, for which we know there is a solution method.

Suppose \(2x+7>0\), i.e. \(x> -{{7}\over{2}}\). Then we get \(2<-9(2x+7)\).
When we move everything with \(x\) to the left and all constant terms to the right, we get \(18x<-65\).
Then, dvision by the coefficient of \(x\)gives \(x < -{{65}\over{18}}\).
So we have the following system of inequalities: \(x> -{{7}\over{2}}\,\wedge\; x < -{{65}\over{18}}\)
and this simplifies to \(\text{an empty solution set}\).

Suppose \(2x+7<0\), i.e. \(x< -{{7}\over{2}}\). Then we get \(2>-9(2x+7)\).
When we move everything with \(x\) to the left and all constant terms to the right, we get \(18x>-65\).
Then, division by the coefficient of \(x\) gives \(x > -{{65}\over{18}}\).
So we have the following system of inequalities: \(x< -{{7}\over{2}}\,\wedge\; x > -{{65}\over{18}}\)
and this simplifies to \(-{{65}\over{18}}\lt x\lt -{{7}\over{2}}\).

The solution of the original inequality is \(-{{65}\over{18}}\lt x\lt -{{7}\over{2}}\).