 Hi and how are you all today? I am Priyanka and let us discuss the following question it says. Solve 24 x less than 100 when x is a natural number, x is an integer for both these subparts we need to solve the given equation. Before proceeding on we should be well versed with the key idea that is going to help us. It is the rules for solving linear inequalities. Rule 1 says equal numbers may be added to or subtracted from both sides of an inequality without affecting the sign of inequality. That means to both these sides that is the left side and the right side we can add or subtract equal number without affecting the sign of the inequality. This is the sign of the inequality we are talking about. Whereas rule 2 says both sides of an inequality can be multiplied or divided by the same positive number. But when both sides are multiplied or divided by a negative number then the sign of the inequality refers. So these are the two rules that will be helping us in solving the inequality given to us. Let us start with our solution. The inequality given to us is 24 x less than 100. Now we are required to find the values for x when x is a natural number and x is an integer. Now 24 x less than 100 on dividing by the same positive 24 number we get. Here we have divided 24 to both sides and hence we have used rule 2 that we discussed in our key idea. So on doing so we have the value of x as x is less than 25 by 6. Now when x is a natural number then the solution set will be 1, 2, 3, till 4. Right? Because by substituting these values here it will make the given inequality true. As we know that 25 divided by 6 is 4 point something so x has to be less than 4 point something and since we are given here that it is a natural number so it will be starting from 1, 2 and goes on till 4. Hence this is the solution set for the first part. The second part when x is an integer the values of x will be all the natural numbers that is for sure make it a whole number and then the negative numbers also. So the negative numbers can be written to as many as we can as it does not have an end point we will end up writing this answer to be our solution set for the second part. Right? So when x is a natural number our solution set are having elements 1, 2, 3, 4 and when x is an integer the values of x are 4, 3, 2, 1, 0, minus 1, minus 2, minus 3 and so on. Right? So this completes the question that was given to us. I hope you enjoyed the session. Do remember the rules and bye for now.