a)Rearrange the folowing to make m the subject; 4(m-2) = t(5m+3)

(Question on topic of algebra taken from June 2016 OCR Past Paper)a) This question LOOKS like algerba and IS 100% algebra. We have 2 unknows that we treat just like we treat any number and we have to make m (specifically) the subject of this equation. Making something the subject is a fancy way of saying "something = ". In this case we need to end up with an equation that has m = ... . As soon as we recognise the topic of algebra we must think of BIDMAS (BODMAS) and rearranging. And so, our precdicted answer has only one m (m=...)but our question has 2 which is an indication we need to "collect terms" or rearrange - meaning bring both m's on the same side of the equals sign. Using BIDMAS we see brackets come first so we should deal with them first -> 4m - 8 = 5tm + 3t. (use arrows to explain) Now, rearranging to collect the m terms to one side. -> 4m-5tm = 3t + 8. (It important to note here that it dosent matter that t is on the other side as well, as long as all m's are on the same side since m is what we're after). From here we can "take m out". This is the opposite of multiplying out a bracket like we've done previously. As an example 4(a+b) multiplied out gives 4a + 4b. Because of the common factor 4 we can "take 4 out", reverse the process we just did -> 4a+4b becomes 4(a+b) (use arrows on board to explain). Returning to our example, our common factor is m so we can do the exact same thing -> m(4-5t) = 3t + 8. Now we only have one m in our equation which means we can achieve our intended equation m= ... .Remember if there's a bracket, that brakect is treated as one term until it is multiplied out. Hence we can easily rearrange to get -> m = (3t + 8)/ (4-5t)