 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that solve for x and check. The equation given is 3 by 4 into 2x plus 1 the whole minus 4 by 3 into x minus 1 the whole is equal to 2 into x by 2 plus 5 by 3 the whole. Let us start with the solution of the given question. Here we are given the equation 3 by 4 into 2x plus 1 the whole minus 4 by 3 into x minus 1 the whole is equal to 2 into x by 2 plus 5 by 3 the whole. Now let us solve this equation for x. First of all we remove the grouping symbol parenthesis and here we get 3 by 4 into 2x that will be equal to 3 by 2x plus 3 by 4 into 1 that is 3 by 4 then we have minus 4 by 3 into x that is minus 4 by 3x minus 4 by 3 into minus 1 that is plus 4 by 3 and this is equal to 2 into x by 2 that is x plus 2 into 5 by 3 that is 10 by 3. Since fractions are involved in this equation so we will multiply all the terms of the equation by least common denominator on both sides of the equation. Now here we can see that least common denominator of all the denominators here that is of 2, 3 and 4 will be 12 so we multiply each term of the equation by 12 we get 12 into 3 by 2x plus 12 into 3 by 4 minus 12 into 4 by 3x plus 12 into 4 by 3 is equal to 12 into x that is 12x plus 12 into 10 by 3 which further implies that 6 into 3x is 18x plus 3 into 3 is 9 minus 4 into 4x is 16x plus 4 into 4 is 16 is equal to 12x plus 4 into 10 is 40. Now here combining all the like terms we get 18x minus 16x plus 9 plus 16 is equal to 12x plus 40 which implies that 2x plus 25 is equal to 12x plus 40. Now we bring variable terms on one side of the equation and constant terms on the other side and we get 2x minus 12x is equal to 40 minus 25 which implies that minus 10x is equal to 15. Now dividing both sides by minus 10 we get minus 10x upon minus 10 is equal to 15 upon minus 10 which implies that x is equal to minus 15 by 10 that is minus 3 by 2 so x is equal to minus 3 by 2. Now we will check whether x is equal to minus 3 by 2 is the solution of the equation or not so we put x is equal to minus 3 by 2 in the original equation that is this equation we get 3 by 4 into 2 into minus 3 by 2 plus 1 the whole minus 4 by 3 into minus 3 by 2 minus 1 the whole is equal to 2 into minus 3 by 2 upon 2 plus 5 by 3 the whole which implies that 3 by 4 into minus 3 plus 1 the whole minus 4 by 3 into minus 3 minus 2 whole upon 2 the whole is equal to 2 into minus 3 by 4 plus 5 by 3 the whole which further implies that 3 by 4 into minus 3 plus 1 is minus 2 minus 4 by 3 into minus 5 by 2 is equal to 2 into minus 9 plus 20 upon 12 this implies that 3 by 2 into minus 1 is minus 3 by 2 minus 2 by 3 into minus 5 is plus 10 by 3 and this is equal to 2 into 11 upon 12 which further implies that now here taking LCM we get 6 in the denominator and in the numerator we have minus 9 plus 20 which is equal to 11 upon 6 now here 11 upon 6 is equal to 11 upon 6 thus left hand side of the equation is equal to the right hand side of the equation so we can say that x is equal to minus 3 by 2 is the solution of the given equation which is the required answer this completes our session hope you enjoyed this session