 Hi and how are you all today? Let us do the question together. It says write the following as intervals. Now these are the four parts of the question which are given to us and we need to write them in intervals. So first let us know what does it mean by interval. Intimual is a set of real numbers which is denoted by A and B. Now here A is less than B and they both are real numbers. Now if we are writing A comma B in brackets like this it is called open interval which is usually written as x is 2. A, x is greater than A is less than B whereas when we write it as in square brackets basically braces it is called closed interval where x is greater than equal to A and it is less than equal to B. So can you find out the difference between open interval and closed interval? Yes in here it is always less than or greater than but here it is less than equal to and greater than equal to also. So let us start with our parts using the key idea which is mentioned by me just now. So the first part is x is 2x belongs to R where x is greater than minus 4 but less than equal to 6. Now here the interval is from minus 4 to 6 where 6 is included but minus 4 is excluded from the interval. Thus this is an open from one side and closed from the other side. So interval will be written as minus 4 it is open from one side but it is closed from the other side as it is less than greater than equal to. So this becomes the answer of our first part. Proceeding on to the second part here we are given x belongs to R minus 12 is less than x and it is less than minus 10. So the interval is from minus 12 to minus 10 where both minus 12 and minus 10 are not included hence it is an open interval. So we will be using these braces and the interval will be written as minus 12 minus 10 in this type of bracket. So this becomes the answer of our second part. Proceeding on to the third part we are given x is 2x belongs to R 0. Now here the interval is from 0 to 7 where 0 is included but 7 is excluded. So that means it is open from one side but closed from another side and hence the interval will be written as 0 7 it is closed from this side but open from this side. So this becomes our answer of the third part. Proceeding on to the last and final part it is x is 2x belongs to R where x is greater than equal to 3 but less than equal to 4. Now here the interval is from 3 to 4 where both 3 and 4 are included that means it's a closed interval from both the sides and hence the answer will be 3, 4 and it's closed from both the sides. So this becomes the answer of the last and final part. So in this question we use the concepts of intervals in the set of real numbers and learned how to write the intervals of the given set. So I hope you enjoyed the session. Bye for now.