 Hello and welcome to the session. In this session we shall discuss the following question and the question says that Two friends, Bob and Oliver are playing video games. Bob scores 5 points more than Oliver. The maximum points they can score is 15 in all. What are the maximum points that can be scored by Bob represent the solution on the number line? Let us move on to the solution. In this question we are given that two friends Bob and Oliver are playing video games. Bob scores 5 points more than Oliver and the maximum points they can score is 15 in all. And we need to find the maximum points that can be scored by Bob and we shall represent the solution on the number line. So here let Oliver score x points as Bob scores 5 points more than Oliver. Therefore Bob score would be x plus 5 points. Now total number of points they both score together will be given by x plus x plus 5 which is equal to 2x plus 5 points. Now according to the question maximum points they both can score is given by 15 in all that is their points must be less than or equal to 15 and not more than that. Hence total points scored by Bob and Oliver should be less than or equal to 15 and we know that total points scored by Bob and Oliver will be given by 2x plus 5 and 2x plus 5 should be less than or equal to 15. Now to find Bob's points we will have to find x that is Oliver's points and to find Oliver's points we shall solve this inequality. For this we subtract 5 from both the sides of the inequality that is we have the inequality 2x plus 5 is less than or equal to 15 and we subtract 5 from both the sides we get 2x is less than or equal to 15 minus 5 that is 10. Now again to keep x alone on one side of the inequality we divide both the sides by 2 and we get 2x by 2 is less than or equal to 10 by 2 which is equal to x is less than or equal to 5. We mark this inequality as 1 since x is Oliver's score so we can say Oliver can score less than or equal to 5 points. With the help of Oliver's score we can find out Bob's score since Bob's score is given by x plus 5 points so we make x plus 5 in inequality 1 to know minimum points scored by Bob that is we have the inequality that if x is less than or equal to 5 and to make it x plus 5 we add 5 on both the sides and we get x plus 5 is less than or equal to 5 plus 5 which implies that x plus 5 is less than or equal to 10 that is Bob can score points less than or equal to 10 and this is the required solution and now we shall represent Oliver's score and Bob's score on the number line. This is the required number line in which positive integers are marked to the right of 0 and negative integers are marked to the left of 0. First we shall represent Oliver's score which is given by the inequality x is less than or equal to 5 here on the number line we mark 5 with the closed dot since Oliver's scores 5 points are less than 5 points in the game. Therefore to represent Oliver's score which is given by the inequality x is less than or equal to 5 we shade all the numbers to the left of 5 on the number line. Since Bob scores 5 points more than Oliver and his score is given by the inequality that is x plus 5 is less than or equal to 10. Since Bob scores 5 points more than Oliver therefore we move 5 positions to the right of 5 and reach 10 and we mark 10 with a closed dot and we shade the number line to the left of 10. It shows points scored by Bob that are represented by the inequality x plus 5 is less than or equal to 10 and this is how we represented Oliver's score and Bob's score on the number line. This completes our lesson. Hope you enjoyed this lesson.