$$\frac{3t-w}{4w}\ge-7$$
$\left\{\begin{matrix}w\geq -\frac{t}{9}\text{, }&t<0\\w\leq -\frac{t}{9}\text{, }&t>0\\w<0\text{, }&t\leq 0\\w=-\frac{t}{9}\text{, }&t\neq 0\\w>0\text{, }&t\geq 0\end{matrix}\right.$
$\left\{\begin{matrix}t\leq -9w\text{, }&w<0\\t=-9w\text{, }&w\neq 0\\t\geq -9w\text{, }&w>0\end{matrix}\right.$