 Hi and welcome to the session. I am Kanika and I am going to help you to solve the following question. The question says solve the following inequality graphically in two dimensional plane. X plus Y is less than 5. Before solving this question we should know that a line divides the Cartesian plane into two parts. Each part is known as a half plane. A vertical line will divide the plane in left half plane and right half plane. And the non-vertical line will divide the plane into lower half plane. The inequality will be one of the half plane. We should show the solution by shading in the corresponding half plane. The following rules to identify the half plane represented by an inequality. 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. Satisfies the inequality, inequality particular containing the point. Not satisfies the inequality represents the solution. So in the first rule we have to take any point AB not on the line and check whether it satisfies the inequality or not. If it satisfies the inequality then the inequality represents that particular half plane containing the point. If it does not satisfies the inequality then the other half plane represents the solution. According to the second rule if sign of equality is also there with inequality is also included in the solution region. We draw in the solution region. And according to the third rule we have a pure inequality responding line in the solution region. We draw a dotted line. With the help of these rules we will identify the half plane represented by an inequality. So always remember these rules. Now begin with the solution. Given inequality is x plus y is less than 5. Therefore the corresponding equation is x plus y is equal to 5. Now we will plot the graph of this equation. Now for plotting the graph we need at least two solutions of this equation. So let's first find the two solutions of this equation. Now when x is equal to 0 then y is equal to 5. And when y is equal to 0 then x is equal to 5. Now these two points satisfy this equation. So let's now plot the points 0 5 and 5 0 on the graph. Now this is the Cartesian plane. We have drawn the two axes x and y. These two axes are perpendicular to each other. We have marked the positive numbers to the right of the origin and negative numbers to the left of the origin on the x axis. And we have marked the positive numbers above the origin and negative numbers below the origin on the y axis. Now we will plot the points 0 5 5 0. Now the first point is 0 5. This means when epsilon is 0 then ordinate is 5. This means this is the required point 0 5. Now we will plot the point 5 0. This means when ordinate is 0 then abscissa is 5. This is the required point 5 0. Now we will join these two points by a line. In the question we are given the inequality x plus y is less than 5 which does not contain the sign of equality. Therefore line AB will not be included in the solution vision and thus it will be shown by a dotted line. Now this line AB divides the plane into two half planes. Now to identify the half plane represented by an inequality x plus y is less than 5 we will take the point 0 0 not lying on the line. And now we will substitute this point in the given inequality. So by substituting this point we get 0 plus 0 is less than 5. So this implies 0 is less than 5 which is true. Hence half plane containing 0 0 represents the inequality x plus y is less than 5. Now this line AB has divided this plane into two parts first and second as the point 0 0 satisfies the given inequality. So this means the first half plane excluding the line AB is the required graphical solution. Now this shaded half plane represents the graph of x plus y less than 5. So this completes the session. Bye and take care.