 Hello and welcome to the session. In this session we are going to discuss how in equations are represented on the number line. To grasp a solution on the number line first mark off the edge of the solution. If the edge is not included then it is marked by an open dot. For example if the inequality says x is greater than 3 then 3 is the edge of the solution and it is not included. Therefore it is marked with an open dot and the number line to the right of 3 is shaded or highlighted. And if the edge is included then mark it with a closed dot. For example if the inequality says x is greater than equal to 3 then 3 is the edge of the solution and it is marked with a closed dot and number line to the right of 3 is shaded or highlighted. Now let us take an example for this. Consider the inequality minus 2 is less than x less than equal to 4. To grab the solution of this on the number line first draw the number line then mark the edges. As this inequality has two edges minus 2 and 4 mark minus 2 as an open dot as x is greater than minus 2 and mark 4 as closed dot as x is less than equal to 4. Now shape the portion between 2 and 4. Let us now discuss the pavement set. Consider the inequality x is greater than or equal to minus 2 where it is an integer. The solution for this is minus 2 minus 1 0 1 2 3 and so on they are given set A equal to minus 4 minus 3 minus 2 minus 1 0 1. Then the elements satisfying the inequality are minus 2 minus 1 0 1 so x is equal to minus 2 minus 1 0 1. Here the replacement set solution for the replacement set is x is equal to minus 2 minus 1 0 1. So the set of elements are possible values any one of which may be used to replace a given variable in a linear inequality. A replacement set as we know that the solution set is the set of all possible values of a variable which satisfy a given n equation. Therefore the solution set is a subset of the given replacement set consisting of those values of the variable which satisfy the given equation. For example if 2 plus x greater than 5 is the given inequality let set A equal to 0 1 3 5 7 9 is the replacement set. Then in the n equation 2 plus x is greater than 5 subtract 2 from both the sides 2 plus x minus 2 is greater than 5 minus 2. Which implies that x is greater than 3 from this the solution set is equal to 5 7 9 this complete 5 version hope you enjoyed this version.