## Precalculus (6th Edition) Blitzer

Let us consider the inequality $5x+4<8x-5$ Take variables on one side, \begin{align} & 5x+4<8x-5 \\ & 4+5<8x-5x \\ & 9<3x \end{align} On dividing both sides by 3, we get, \begin{align} & 3\lt x \\ \end{align} During the whole solution, there is no need to divide by a negative number. Therefore, the solution can be determined without division by a negative number.