solve: [(3x-2)/4] - [(2x+5)/3] = [(1-x)/6]

On the first look, you may think that this question looks a bit complex, but if you have ,mastered the basics then you will have absolutely no trouble! Before you jump into this question, you should start by recognising the skills that you are being examined on. In this case, it is your ability to add fractions, expand brackets and deal with algebra i.e. moving numbers and unknowns across the equals sign, from one side of the equation to the other. In order to add fractions (and subtract fractions for that matter), remember that you must have the same common denominator. Therefore, in this case, we need to make a common denominator for all 3 components/ fractions of the question. The lowest common multiple for the denominators we have, i.e. 3, 4 and 6 would be the number 12- therefore, we should make 12 the common denominator.For the denominator of the first fraction - we are multiplying the 4 by 3 to get to 12, and what we do to the bottom of the fraction we must also do to the top of the fraction, so we must multiple the top line by 3 also. For the denominator of the second fraction - we are multiplying the 3 by 4 to get to 12, and what we do to the bottom of the fraction we must also do to the top of the fraction, so we must multiple the top line by 4 also. For the denominator of the third fraction - we are multiplying the 6 by 2 to get to 12, and what we do to the bottom of the fraction we must also do to the top of the fraction, so we must multiple the top line by 2 also. Once we have the same denominator on all of the fractions on the left and right of the equals sign- we can ignore the denominators and just focus on the top line of the fractions in order to get our value for x.So now we have: 3(3x - 2) - 4(2x + 5) = 2(1-x). Now, the question is testing your ability to expand brackets, so you must be very careful when dealing with the negative and positive signs! Remember that multiplying -4 with +5 will give you -20, not +20!When expanding this correctly, you should get: 9x - 6 - 8x - 20 = 2 - 2x Now, what you should do is put all of the unknowns on the left of the equals sign, and all of the known constants on the right of the equals sign. Remember that the sign for the numbers switches when you move them across the equals sign!After doing this, you should get 9x - 8x + 2x = 2 + 6 + 20Now, simplify the equation to get: 3x = 28To get x on its own, we need to divide the 3x by 3 to get rid of the 3, and remember that what we do to the left hand side, we must also do the exact same on the right hand side, so we must also divide the right hand side by 3.Therefore, you will get x = 28/3 The question did not specify that the answer should be in a particular form i.e. as a mixed fraction, therefore, you can leave your answer like this! But it is good practice to make sure your answer is in its simplest form, which in this case, it is!