 Hi, and welcome to the session. Let's discuss the following question. The question says solve the following inequality graphically in two-dimensional plane. Minus 3x plus 2y is greater than equal to minus 6. Before solving this question, we should know that a line divides the Cartesian plane into two half planes. And the graph of inequality will be one of the half planes. And we shall show the solution by shading in the corresponding half plane. We shall follow the following rules to identify the half plane represented by an inequality. According to the first rule, we will take any point A, B, not on the line, and then we will check whether it satisfies the inequality or not. If this point satisfies the inequality, then the inequality represents that particular half plane containing the point. And if it does not satisfy the inequality, then the other half plane represents the solution. And according to the second rule, if sign of equality is also there with the inequality, then the line is included in the solution region, and so we draw a dotted line. And according to the third rule, if we have a pure inequality, then the points on the corresponding line are not to be included in the solution region, and so we draw a dotted line. With the help of these three rules, we will solve this question. So always remember these rules. The solution given inequality is minus 3x plus 2y is greater than equal to minus 6. Now converting this in equation into equation, we get minus 3x plus 2y is equal to minus 6. Now we have to plot the graph of this equation. For plotting the graph, we need at least two solutions of this equation. So let's first find the two solutions of this equation. If x is equal to 0, then y is equal to minus 3, and if y is equal to 0, then x is equal to 2. So the two solutions of this equation are 0, minus 3, and 2, 0. Now we will plot these two points on the graph. So let's make a graph now. The two points which we have to plot are 0, minus 3, and 2, 0. Now the first point is 0, minus 3. This means when fc psi is 0, then ordinate is minus 3. So this is the required point, 0, minus 3. And the second point is 2, 0. This means when ordinate is 0, then fc psi is 2. So this is the required point, 2, 0. By the second rule, we know that if we have a sign of equality with inequality, then the line is included in the solution region, and so we draw a dark line. Now in this question, we have minus 3x plus 2y is greater than equal to minus 6. The sign of equality is there. So this means we will join these two points by a dark line, and this line will be included in the solution region. So let's now join these two points. This line is representing the equation minus 3x plus 2y is equal to minus 6. And this line divides the plane into two half planes, that is 1 and 2. We have to identify the half plane represented by the given equality. According to the first rule, we have to select a point which does not lie on the line, and then we have to check whether it satisfies the inequality or not. If this point satisfies the inequality, then the inequality represents that particular half plane, which contains the point. And if it does not satisfy the inequality, then the other half plane represents the solution. As the point 0, 0 does not lie on this line, so we will take the point as 0, 0. Now, substitute this point in the given inequality. By substituting, we get 0 greater than equal to minus 6, which is true. Half plane containing 0, 0 represents the inequality minus 3x plus 2y is greater than equal to minus 6. And there is the solution region. Let's look at the graph. Half plane contains the point 0, 0. And in the question, we have minus 3x plus 2y is greater than equal to minus 6. We have a sign of equality also. So this means the solution region will consist of first half plane and this line. So let's now shade this half plane. This is the required solution region. The shaded half plane, including the line, is the required graphical solution. This is our required answer. So this completes the session. I am taking care.