We note first that division by zero is not allowed and that for this reason \(6x-8\) may not be equal to zero and that therefore \(x={{4}\over{3}}\) is not a solution.

We now distinguish two cases, namely \(6x-8>0\) and \(6x-8<0\).
In both cases we multiply the inequality on both sides by \(6x-8\) because we then get a linear inequality, for which we know there is a solution method.

Suppose \(6x-8>0\), i.e. \(x> {{4}\over{3}}\). Then we get \(7<4(6x-8)\).
When we move everything with \(x\) to the left and all constant terms to the right, we get \(-24x<-39\).
Then, dvision by the coefficient of \(x\)gives \(x > {{13}\over{8}}\).
So we have the following system of inequalities: \(x> {{4}\over{3}}\,\wedge\; x > {{13}\over{8}}\)
and this simplifies to \(x\gt{{13}\over{8}}\).

Suppose \(6x-8<0\), i.e. \(x< {{4}\over{3}}\). Then we get \(7>4(6x-8)\).
When we move everything with \(x\) to the left and all constant terms to the right, we get \(-24x>-39\).
Then, division by the coefficient of \(x\) gives \(x < {{13}\over{8}}\).
So we have the following system of inequalities: \(x< {{4}\over{3}}\,\wedge\; x < {{13}\over{8}}\)
and this simplifies to \(x\lt {{4}\over{3}}\).

The solution of the original inequality is \(x\lt {{4}\over{3}}\;\vee\;x\gt{{13}\over{8}}\).