 Hi, and welcome to the session. Let's discuss the following question. The question says, solve the following inequality graphically in two-dimensional plane. Why is less than minus 2? 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 have to take any point a being not on the line. And then we have to take whether it satisfies the inequality or not. If that point satisfies the inequality, then the inequality represents that particular half plane containing the point. But if the point does not satisfy the inequality, then the other half plane represents the solution. And according to the second rule, if the sign of equality is also there with the 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 point in 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 these questions. So always remember these rules. Let's now begin with the solution. Given inequality is y is less than minus 2. Now converting this inequality into equation, we get y is equal to minus 2. Now we have to plot the graph of this equation. The two solutions of this equation are minus 2, minus 2, and 2, minus 2. 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 minus 2, minus 2, and 2, minus 2. The first point is minus 2, minus 2. This means when epsilon is minus 2, then ordinate is also minus 2. This is the required point, minus 2, minus 2. Second point is 2, minus 2. This means when epsilon is 2, then ordinate is minus 2. So this is the point 2, minus 2. According to the third 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. Now in this question, we have y less than minus 2. We have a strict inequality, so that means we will join these two points by a dotted line. And this line will not be included in the solution region. So let's now join these two points. This line is parallel to x-axis, and this line is dividing the plane into two half planes, that is 1 and 2. Now we have to identify the half plane represented by the given inequality. 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 this point satisfies the given inequality or not. If that point satisfies the given inequality, then the inequality represents that particular half plane containing the point. But if the point does not satisfy the given inequality, then the other half plane, that means the half plane which does not contain the point, represents the inequality. As the point 0, 0 does not lie on the line, so we can take the point as 0, 0. Substituting the point in the given inequality, we get 0 less than minus 2, which is not true. The half plane not containing 0, 0 represents the inequality while less than minus 2. Now let's look at the graph. Second half plane does not contain the point, 0, 0. So this means the solution region of the given inequality consists of second half plane. And as we have a stricter inequality, so this line will not be included in the solution region. Let's now shade this region. This is the required solution region. The shaded excluding the line required graphical solution. This is our required answer. So this completes the session. Bye, and take care.