We note first that division by zero is not allowed and that for this reason \(4x-9\) may not be equal to zero and that therefore \(x={{9}\over{4}}\) is not a solution.

We now distinguish two cases, namely \(4x-9>0\) and \(4x-9<0\).
In both cases we multiply the inequality on both sides by \(4x-9\) because we then get a linear inequality, for which we know there is a solution method.

Suppose \(4x-9>0\), i.e. \(x> {{9}\over{4}}\). Then we get \(8<6(4x-9)\).
When we move everything with \(x\) to the left and all constant terms to the right, we get \(-24x<-62\).
Then, dvision by the coefficient of \(x\)gives \(x > {{31}\over{12}}\).
So we have the following system of inequalities: \(x> {{9}\over{4}}\,\wedge\; x > {{31}\over{12}}\)
and this simplifies to \(x\gt{{31}\over{12}}\).

Suppose \(4x-9<0\), i.e. \(x< {{9}\over{4}}\). Then we get \(8>6(4x-9)\).
When we move everything with \(x\) to the left and all constant terms to the right, we get \(-24x>-62\).
Then, division by the coefficient of \(x\) gives \(x < {{31}\over{12}}\).
So we have the following system of inequalities: \(x< {{9}\over{4}}\,\wedge\; x < {{31}\over{12}}\)
and this simplifies to \(x\lt {{9}\over{4}}\).

The solution of the original inequality is \(x\lt {{9}\over{4}}\;\vee\;x\gt{{31}\over{12}}\).