Represent to solution set of each of the following inequations graphically in two dimensional plane:

Converting the inequation to equation, we obtain $-3 x+2 y=6$, i.e $-3 x+2 y-6=0$

Putting y = 0 and x = 0 in this equation, we obtain x = -">−-2 and y = 3 respectively. So, this line meets the x-axis at (-">−-2,0) and the y-axis at (0,3).

We plot these points and join them by a thick line.This divides the xy plane in two parts. To determine the region represented by the given inequality, consider point $O(0,0)$. Clearly, $(0,0)$ satisfy the inequality $-3 x+2 y \leq 6$. So, the region containing the origin is represented by the given inequality.

Hence, the shaded region is the solution to the inequation.