 Hello and welcome to the session. In this session we are going to discuss the following question. And the question says that, represent the given intervals graphically. First, x is greater than 5. Second, minus 2 is less than x is less than equal to 3. Third, x is less than equal to minus 1. Now let us start with the solution of the given question. Now in the first part of the question, we are given the inequality x is greater than 5. We have to represent it on the number 9. Now for x is greater than 5, we will darken that portion of the number line which represents numbers greater than 5 i.e. to the right of 5. First of all, we shall plot the 0.5 on the number line, then darken the number line to the right of 5. Since in the inequality, we have greater than sign which means 0.5 is not included in the interval. To represent this, we will put a hollow circle at 5. Now this is the graph of the inequality x is greater than 5 i.e. this blue shaded portion of the number line represents this inequality. Now we move on to the second part of the question. In this part, we are given the inequality minus 2 is less than x is less than equal to 3. It means x is greater than minus 2 and x is less than or equal to 3. First we plot minus 2 and 3 on the number line. Since x is greater than minus 2 and less than or equal to 3. To represent this, we darken the portion of number line in between minus 2 and 3. Now with minus 2, we have less than sign and with 3 we have less than equal to sign. To represent this, we put a hollow circle at minus 2 and a dark circle at 3. This means minus 2 is the excluded point and 3 is the included point. Hence we have represented the given inequality on the number line. The red shaded portion of the number line represents this given inequality. Now in the third part of the question, we are given the inequality x is less than equal to minus 1. For this, first we plot minus 1 on the number line. Now we are given that x is less than or equal to minus 1. So first we will darken all the portion of number line to the left of minus 1. In this inequality, less than or equal to sign is given which means that minus 1 is the included point. So to represent this, we put a dark circle at minus 1. So this yellow shaded portion of the number line represents the inequality except less than equal to minus 1. This is the solution of the given question. This completes our session. Hope you enjoyed this session.