 Hello and welcome to the session. In this session, we are going to discuss the following question and the question says that solve and graph the solution set of 3x minus 10 less than 8 or 2x plus 10 greater than equal to 26 for x belonging to R, the set of real numbers. Let A be the set of all x such that 3x minus 10 is less than 8 for x belonging to R and B be the set of all x such that 2x plus 10 is greater than equal to 26 for x belonging to R. First let us consider the in equation 3x minus 10 less than 8. As adding or subtracting any real number to an inequality does not change the inequality, so we add 10 on both sides of the in equation. So the in equation becomes 3x minus 10 plus 10 is less than 8 plus 10. This implies 3x is less than 18. This implies x is less than 18 by 3 which is equal to 6 which is obtained on dividing the whole in equation by 3. So we have x is less than 6 that is the set A is equal to all those x such that x is less than 6 for x belonging to R the set of real numbers. Now consider the in equation 2x plus 10 is greater than equal to 26. As we know on subtracting any positive real number from both sides of the in equation will not change the in equation so we subtract 10 on both sides of the in equation. So the in equation becomes 2x plus 10 minus 10 is greater than equal to 26 minus 10. This implies 2x is greater than equal to 16. That is x is greater than equal to 16 upon 2 which is equal to 8 which is obtained on dividing the whole in equation by 2. So the set B is equal to all those x such that x is greater than equal to 8 for x belonging to R the set of real numbers. As we have to find the solution set of 3x minus 10 less than 8 or 2x plus 10 is less than equal to 26. So we find the union of A and B as or means union. Therefore A union B is equal to the set containing all x such that x is less than 6 for x belonging to the set of real numbers union. The set containing x such that x is greater than equal to 8 for x belonging to the set of real numbers. Now let us graph the solution set of A union B on the number line. Draw a number line and mark all points 0, 1, 2, 3, 4 and so on and minus 1, minus 2, minus 3 and so on on the number line on equal distances. As x is strictly less than 6 so we mark 6 with an open dot as 6 will not be included in the solution set. Now shade the number line on the left of 6 as x is less than 6. Also x is greater than equal to 8 so mark 8 with a closed dot as 8 will be included in the solution set. Now shade the number line on the right of 8 as x is greater than equal to 8. Hence the graph of A union B is shown by the yellow shaded portion on the number line. This completes our session. Hope you enjoyed the session.