Rearrange the following to make m the subject. 4(m – 2) = t (5m + 3)

In this equation we have two variables (meaning a symbol - usually denoted by a letter - which represents varying values) ‘m’, and ’t’. The question is asking us to make m the subject of this equation which means we want to be left with an equation which looks like ‘m = [an expression containing t]’. So, how do we take an equation which has two ‘m’ variables and turn it into one ‘m’ variable equaling ‘[an expression containing t]’? The first thing we want to do is expand the brackets, that will make the manipulation of these numbers and letters much easier. So: 4(m – 2) = t (5m + 3) goes to 4m - 8 = 5mt + 3tNow we want to take the ‘m’ variables to one side and the ’t’ variables to the other, but what are we meant to do with our ‘5mt’ value which has both variables in? Well we should be able to recognise that with factorisation we can isolate the ‘m’ variable so that we’re left with an ‘m = [t]’ expression. So:4m - 8 = 5mt + 3t goes to 4m - 5mt = 3t + 8 (double check you haven’t made a sign error!)Note we took ‘5mt’ to the left rather then factorising ’t’ out of the right hand side, as it allows us to be left with a single ‘m’ variable instead of a nasty fraction with multiple ‘m’ variables (once rearranged). So:Factorising out the ‘m’ we get: m(4 - 5t) = 3t + 8 Now all that’s left to do is make ‘m’ the subject by dividing both sides by (4 - 5t). Therefore our final solution is: m = (3t + 8)/(4 - 5t)