Precalculus (6th Edition) Blitzer

Let us consider the first inequality and put a test point $\left( 0,0 \right)$ in this inequality to check whether it satisfies the inequality or not as given below: \begin{align} & y\ge 6x-24 \\ & 0\ge 0-24 \\ & 0\ge -24 \\ \end{align} Which is correct. Thus, the test point $\left( 0,0 \right)$ satisfies the inequality and the shaded region will be towards the origin. Also, consider the second inequality and put a test point $\left( 0,0 \right)$ in this inequality to check whether it satisfies the inequality or not as given below: \begin{align} & y\lt6x-24 \\ & 0\lt0-24 \\ & 0\lt -24 \\ \end{align} Which is false. Thus, there is no solution.