 Hi and welcome to our session. Let us discuss the following question. The question says solve the calling inequality graphically in two-dimensional plane. Given an equation is 3 y minus 5 x less than 30. So solving this question we should note that a line divides the Cartesian plane into two half planes and graph of inequality will be one of the half planes. We shall show the solution by shading in the corresponding half plane. We have learned the rules which are used to identify the half plane represented by an inequality. According to the first rule we have to take any point a be not on line and then we have to check whether it satisfies the inequality or not. If the point satisfies the inequality then the inequality represents that particular half plane containing the point. But if the point not satisfies the inequality then the other half plane represents the solution. And according to the second rule if sign of equality is also there with inequality then the line is included in the solution region and so we draw a dark line. And according to the last rule if we have a pure inequality then the points on the corresponding line are not included in the solution region and so we draw a dotted line. Keeping all these rules in mind let's now begin with the solution. Given an equation is 3 y minus 5 x is less than 30. Now equation corresponding to this inequality is 3 y minus 5 x equals to 0. Now when we find two solutions of this equation put y equals to 0. Now when y is equal to 0 then x is equal to minus x and when x is equal to 0 then y is equal to 10. So the two solutions of this equation are minus 6 0 and 0 10. Now we will plot these two points on the graph so let's make a graph now. Now the two points which we have to plot are 0 10 and minus 6 0. Now the first point is 0 10 this means when fc psi is 0 then ordinate is 10 this is the point 0 10. Second point is minus 6 0 this means when ordinate is 0 then fc psi is minus 6 this is the point minus 6 0. Now according to the last rule we know that if we have a pure inequality then the points on the corresponding line are not included in the solution region and so we draw a dotted line. Now here the given inequality is 3 y minus 5 x is less than 30. We have a pure inequality here so we will draw a dotted line to join these two points and this line will not be included in the solution region. This is the line 3 y minus 5 x equals to 30. Now this line is dividing this plane into two half planes that is first and second. Now we have to identify the half plane represented by the given inequality. Now according to the first rule we have to take any point ab not on the line and then we have to check whether it satisfies the inequality or not. If the point satisfies the inequality then the inequality represents that particular half plane containing the point but if the point not satisfies the inequality then the other half plane represents the solution. Now we will identify the half plane represented by the given inequality. According to the first rule we know that we have to take any point ab not on the line and then we have to check whether it satisfies the inequality or not. If the point satisfies the inequality then the inequality represents that particular half plane containing the point but if the point not satisfies the inequality then the other half plane represents the solution. Now as the point 0 0 does not lie on the line 3 y minus 5 x equals to 0 so we will take the point as 0 0. On substituting x is 0 and y is 0 we get 0 less than 30 which is true the half plane containing 0 0 represents the inequality 3 y minus 5 x less than 30. Half plane contains the point 0 0 so this means this is the required solution region and in this solution region this line will not be included as we have pure inequality. So let's now shade this region. This is the required graphical solution of the given inequality. Therefore the shaded half plane first excluding the line is the required graphical solution. This is our required answer. So this completes the section. Bye and take care.