 Hello and welcome to the session. In this session, we are going to discuss the following question which says that Let us solve the following equations for x and the first part is 3x-8 the whole upon 5 is equal to 4x-8 the whole upon 3 and the second part is 3 into x plus 1 the whole minus 5 is equal to 3x-2. Let us start with the solution. In the first part of the question, we are given the equation that is 3x-8 the whole upon 5 is equal to 4x-8 the whole upon 3 and you need to solve this equation for x. So we can simplify this equation by using graph multiplication and we write 3 into 3x-8 the whole is equal to 5 into 4x-8 the whole. That is 3 into 3x is equal to 9x-3 into 8 is 24 is equal to 5 into 4x that is 20x-5 into 8 that is 40. On solving further we get 9x-20x is equal to minus of 30 plus 24 which implies that 9x-20x is equal to minus of 11x which is equal to minus 30 plus 24 that is minus of 16. Which implies that x is equal to minus of 16 upon minus of 11. Therefore we say that x is equal to 16 by 11 and we can also write it as in the form of mixed fraction as 1 and 5 by 11. So we say that the given equation has only one solution given by x is equal to 1 and 5 by 11 which is the required answer. Now we move on to the second part of the question and we need to solve this equation for x and the equation is 3 into x plus 1 the whole minus 5 is equal to 3x minus 2. Now we simplify this equation and by using distributive property in the left hand side of the equation we get 3 into x plus 3 into 1 minus of 5 is equal to 3x minus 2. We know that if we have any expression of the form a into b plus c the whole then by using distributive property it can be written as a into b plus a into c. Now on solving further we get 3 into x is 3x plus 3 into 1 that is 3 minus of 5 is equal to 3x minus 2 which implies that 3x plus 3 minus 5 can be written as minus 2 is equal to 3x minus 2. Now subtracting 3x from both the sides we get 3x minus 2 minus of 3x and is equal to 3x minus 2 minus of 3x which implies that minus 2 is equal to minus 2. Or we can write it as 2 is equal to 2 which is true for all x so the equation will have in finitely many solutions which is the required answer. This complete file session hope you enjoyed this session.