 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that, solve the following in equation 4x minus 3 upon 2 plus 6 is greater than equal to 3 plus 8x upon 3 for x belonging to R, the set of real numbers. Consider the given in equation 4x minus 3 upon 2 plus 6 is greater than equal to 3 plus 8x upon 3. Now here the LCM of the LHS is 2 and the LCM of RHS is 3. So on taking the LCM on both the sides we have 4x minus 3 plus 12 upon 2 is greater than equal to 9 plus 8x upon 3 which implies 4x plus 9 upon 2 is greater than equal to 9 plus 8x upon 3. Now the LCM of both the sides that is the LCM of 2 and 3 is 6. So on multiplying both sides by 6 we will have 6 into 4x plus 9 upon 2 is greater than equal to 6 into 9 plus 8x upon 3. This is because if we multiply the whole inequality by a same number then the inequality remains the same. Now this becomes 3 into 4x plus 9 is greater than equal to 2 into 9 plus 8x. On opening the brackets we will have 12x plus 27 is greater than equal to 18 plus 16x. If we add or subtract the same number from both sides of the inequality the inequality will remain the same so we subtract 12x from both sides of the inequality that is we will have 12x plus 27 minus 12x will be greater than equal to 18 plus 16x minus 12x. So this will become 27 is greater than equal to 18 plus 4x. Now again we subtract 18 from both sides of the inequality. We will obtain 27 minus 18 is greater than equal to 18 plus 4x minus 18 which will become 9 is greater than equal to 4x. So we will have x is less than equal to 9 by 4 on dividing the inequality by 4. So we have x is less than equal to 2.25 which is our answer. This completes our session. Hope you enjoyed this session.