 Hello and welcome to the session. In this session we will discuss the following question and the question says solve the inequalities. Part A is 2x plus 5 is less than 17 in the system of natural numbers. Part B, 5x plus 4 is greater than 21 in the system of natural numbers. Part C, 3x plus 7 is greater than equal to 1 in the system of integers. Part D, 4x minus 1 is less than equal to 15 where x belongs to the set containing the elements minus 5, minus 4, minus 2, 0, 1, 3, 5, 9. Let's start the solution now. In part A we have the inequality 2x plus 5 is less than 17. Subtract 5 from both sides so we get 2x plus 5 minus 5 is less than 17 minus 5. Since same quantity is being subtracted from both the sides so the inequality remains same this implies 2x is less than 12 divide both sides by 2 so we get x is less than 12 divided by 2 since both the sides are divided by a positive number so the inequality remains the same. This implies x is less than 6. Now we have to find the solution in the system of natural numbers so we have to find all the natural numbers which are less than 6. We know that natural numbers less than 6 are 1, 2, 3, 4 and 5 hence x is equal to 1, 2, 3, 4, 5. This is our solution for the first part. Now in part B we are given the inequality 5x plus 4 is greater than 21. Subtract 4 from both the sides so we get 5x plus 4 minus 4 is greater than 21 minus 4. Here again there is no change in the inequality because same number is subtracted from both sides. This implies 5x is greater than 17 now divide both sides by 5 so we get 5x by 5 is greater than 17 by 5. This implies x is greater than 17 by 5 which implies x is greater than 3.4. Now we have to find the solution in the system of natural numbers and we know that natural numbers greater than 3.4 are 5, 6, 7, 8 and so on till infinity. Therefore the solution is x is equal to 4, 5, 6, 7, 8 and so on. Now in part C we have the inequality 3x plus 7 is greater than equal to 1. Subtract 7 from both sides so we get 3x plus 7 minus 7 is greater than equal to 1 minus 7. This implies 3x is greater than equal to minus 6. We now divide both sides by 3 so we get 3x divided by 3 is greater than equal to minus 6 divided by 3. Since 3 is a positive number so the inequality remains same this implies x is greater than equal to minus 2. Now we have to find the solution in the system of integers and we know that integers greater than or equal to minus 2 are minus 2 minus 1, 0, 1, 2, 3 and so on till infinity. Therefore the solution is x is equal to minus 2 minus 1, 0, 1, 2, 3 and so on till infinity. In part D we are given the inequality 4x minus 1 is less than equal to 15 where x belongs to the set containing the elements minus 5 minus 4 minus 2, 0, 1, 3, 5, 9. Now we add 1 on both sides so we get 4x minus 1 plus 1 is less than equal to 15 plus 1. Since we have added same number on both sides so the inequality remains the same this implies 4x is less than equal to 16. We now divide both sides by 4 so we get 4x by 4 is less than equal to 16 by 4 since we have divided both the sides by a positive number so the inequality remains the same. This implies x is less than equal to 4. We are given that x belongs to the set containing all these numbers that is x belongs to the set containing the elements minus 5 minus 4 minus 2, 0, 1, 3, 5, 9. Now we choose all those numbers from this set which are less than or equal to 4. These numbers are minus 5 minus 4 minus 2, 0, 1, 3. Therefore the solution is x is equal to minus 5 minus 4 minus 2, 0, 1, 3. With this we end our session. Hope you enjoyed the session.