 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that find the solution set of minus 5 less than 2x minus 4 less than equal to 8 minus x where x belongs to the set of integers also graph the solution set we are given minus 5 is less than 2x minus 4 is less than equal to 8 minus x on separating them as two in equations we get minus 5 is less than 2x minus 4 and 2x minus 4 is less than equal to 8 minus x first consider minus 5 is less than 2x minus 4 as adding or subtracting any number to the in equation will not change the in equation therefore we add 4 on both sides and we get minus 5 plus 4 is less than 2x minus 4 plus 4 this implies minus 1 is less than 2x again dividing the in equation by the same number will not change the in equation so we get x is greater than minus 1 by 2 on dividing the in equation by 2 now consider 2x minus 4 is less than equal to 8 minus x as adding or subtracting the same number on both sides of the in equation will not change the in equation so we add x and 4 on both sides of this in equation we get 2x minus 4 plus x plus 4 is less than equal to 8 minus x plus x plus 4 this implies 3x is less than equal to 12 dividing by 3 on both sides we get x is less than equal to 12 by 3 which is equal to 4 so we get x is less than equal to 4 we have got x is greater than minus half and x is less than equal to minus 4 so x is greater than minus half and x is less than equal to 4 combining the two we have minus half is less than x is less than equal to 4 as x belongs to the set of integers therefore we shall take all the integers greater than minus half and less than equal to 4 so the solution set is equal to 0 1 2 3 and 4 now we shall represent the solution set on the number line mark the points 0 1 2 3 4 5 minus 1 minus 2 minus 3 minus 4 and so on on the number line the solution set consists of the integers 0 1 2 3 and 4 so we mark these points 0 1 2 3 and 4 with closed dots on the number line these points are shown as closed dots on the number line as the number line consists of all real numbers and we have x belongs to the set of integers only this completes our session hope you enjoyed the session