Find the linear inequalities for which the shaded area is the solution set in the figure given below.

We have seen that the shaded region and origin are on the same side of the line

For (0,0) we have . So the shaded region satisfies the inequality .

We have seen that the shaded region and origin are on the same side of the line

For (0,0) we have . So the shaded region satisfies the inequality .

Also , the region lies in the first quadrent . Therefore

and

Thus the linear inequation comprising the given solution set are , , ,