 Hello and welcome to the session. In this session, we discussed the following question that says solve the following linear equation, check the result also. 3 upon 4 into 6x minus 1 minus 2x minus 2 minus x upon 2 is equal to x plus 5 upon 2. Let's move on to the solution now. The given linear equation is 3 upon 4 into 6x minus 1 minus 2x minus 2 minus x upon 2 is equal to x plus 5 upon 2. First we will remove these brackets so we would get 3 upon 4 into 6x plus 3 upon 4 into minus 1 minus 2x plus 2 minus x upon 2 is equal to x plus 5 upon 2. Now 2 times is 4, 2 3 times is 6 so this would give us 9x upon 2 minus 3 upon 4 minus 2x plus 2 upon 2 minus x upon 2 is equal to x plus 5 upon 2. Now we will multiply both sides by the LCM of the numbers 2 and 4 since we have 2 and 4 in the denominators. Thus we say multiplying both sides by 4 which is the LCM of 2 and 4 and I am doing this we get 4 into 9x upon 2 minus 4 into 3 upon 4 minus 4 into 2x plus 4 into 1 that is 2 upon 2 is 1 minus 4 into x upon 2 is equal to 4 into x plus 4 into 5 upon 2. Now 2 2 times is 4, 4 1 times is 4 so 4 cancels with 4 then 2 2 times is 4 and here also 2 2 times is 4. So this gives us 2 multiplied by 9x that is 18x minus 3 minus 4 into 2x that is 8x plus 4 minus 2x is equal to 4x plus 10. Now we transpose the terms containing x from the right hand side to the left hand side so we get 18x minus 3 minus 8x plus 4 minus 2x minus 4x is equal to 10. Next we would transpose the constant terms from the left hand side to the right hand side this gives us 18x minus 8x minus 2x minus 4x is equal to 10 plus 3 minus 4. Now this further gives us 4x is equal to 9 now this gives us x is equal to 9 upon 4 so we have got the value for x as 9 upon 4. Now we are going to check the result. Now substituting x equal to 9 upon 4 in the given equation we get first let's see what would be the LHS. LHS is given as 3 upon 4 into 6x minus 1 minus 2x minus 2 minus x upon 2. Now we substitute x equal to 9 upon 4 in this so this would give us 3 upon 4 into 6 into 9 upon 4 minus 1 minus 2 into 9 upon 4. So minus 2 minus 9 upon 4 whole upon 2. Now 2 2 times is 4 2 3 times is 6 2 2 times is 4 so this would further give us 3 upon 4 into 27 upon 2 minus 1 minus 9 upon 2 minus minus 1 upon 4 upon 2. That is we get 3 upon 4 into 27 minus 2 upon 2 minus 9 upon 2 plus 1 upon 8. This further gives us 3 upon 4 into 25 upon 2 minus. Now we get 8 as the LCM 9 4 times is 36 plus 1 upon 8 so this gives us 75 upon 8 minus 37 upon 8 this is equal to 75 minus 37 upon 8 and this comes out to be equal to 38 upon 8 now 2 4 times is 8 and 2 19 times is 38 so this is equal to 19 upon 4 that is we get the LHS equal to 19 upon 4. Now let's consider the RHS which is x plus 5 upon 2 now we substitute x equal to 9 upon 4 in this so this would be equal to 9 upon 4 plus 5 upon 2. Now this is equal to now the LCM of 214 is 4 so this would be equal to 9 plus 10 upon 4 equal to 19 upon 4 this is the RHS. So as you can see LHS and the RHS are equal hence we say x equal to 9 upon 4 is a solution of the given equation so this completes our session hope you have understood the solution for this question.