 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that what inequality do the following number lines represent? We know that a closed dot on the number line represents that the number is included and an open dot represents that the number is not included in the solution of the given inequality. With this the idea let us proceed to the solution. In the question we need to recognize the inequality represented by the given number lines. In the first part we see that 3 is not with an open dot and the portion on the right of 3 is shaded. This means that all the numbers greater than 3 are included but number 3 is not included since the numbers to the right of 3 are greater than 3 and 3 is marked with an open dot which means 3 is not included. It is clear from the key idea that an open dot represents that the number is not included in the solution of the given inequality. Therefore here number 3 is not included let X be any number and the numbers to the right of 3 are greater than 3 then the inequality represented by this number line will be given by X is greater than 3 and this is the required answer. In the second part we see that minus 2 is marked with a closed dot and the number line is shaded to the left of minus 2 and from the key idea we know that a closed dot on the number line represents that the number is included in the solution of the given inequality. All numbers to the left of minus 2 will be less than minus 2 and the closed dot represents minus 2 is also included. So if X is any number then the inequality represented by this number line is given by X is less than or equal to minus 2. This completes our session hope you enjoyed this session.