We note first that division by zero is not allowed and that for this reason \(4x+5\) may not be equal to zero and that therefore \(x=-{{5}\over{4}}\) is not a solution.

We now distinguish two cases, namely \(4x+5>0\) and \(4x+5<0\).
In both cases we multiply the inequality on both sides by \(4x+5\) because we then get a linear inequality, for which we know there is a solution method.

Suppose \(4x+5>0\), i.e. \(x> -{{5}\over{4}}\). Then we get \(7<6(4x+5)\).
When we move everything with \(x\) to the left and all constant terms to the right, we get \(-24x<23\).
Then, dvision by the coefficient of \(x\)gives \(x > -{{23}\over{24}}\).
So we have the following system of inequalities: \(x> -{{5}\over{4}}\,\wedge\; x > -{{23}\over{24}}\)
and this simplifies to \(x\gt-{{23}\over{24}}\).

Suppose \(4x+5<0\), i.e. \(x< -{{5}\over{4}}\). Then we get \(7>6(4x+5)\).
When we move everything with \(x\) to the left and all constant terms to the right, we get \(-24x>23\).
Then, division by the coefficient of \(x\) gives \(x < -{{23}\over{24}}\).
So we have the following system of inequalities: \(x< -{{5}\over{4}}\,\wedge\; x < -{{23}\over{24}}\)
and this simplifies to \(x\lt -{{5}\over{4}}\).

The solution of the original inequality is \(x\lt -{{5}\over{4}}\;\vee\;x\gt-{{23}\over{24}}\).