Cahsee Math 1.3 Mathematical Reasoning by Shmoop

You look too happy. Here’s an unshmoopy question to take you down a peg… When solving the equation one over x minus one-half equals 3 for x, which of the following is the correct order of steps? And here are the potential answers: OK so this question is just pushing us to think about patterns of problem solving… and it throws in some curves and freebies as well. Note that potential answer B asks about SUBTRACTING a half from both sides – well, since our one-half on the left is already negative, we wouldn’t be able to cancel it out. It would just be useless so we can eliminate option B. Consider just the remaining 3 – and remember that the key goal in solving any of these kinds of problems is to isolate x. If we add a half to both sides – which is the first thing we do in the other potential answers – the new equation looks like this: 1 over x equals 3 plus one-half. So the next step is to just simplify 3 PLUS 1 half to be uh, yeah – 3 and a half. Note that C has you subtracting a half as the second step here – and that’s just wrong – we’ve ADDED a half to both sides; so you can cross out C. So it gets down to D versus A. A suggests taking the RECIPROCAL of the result whereas D asks us to take the OPPOSITE of the result. The… opposite of the result? Not even sure what that would be. Sounds like someone who just landed on our planet and is trying to fit in. Taking the RECIPROCAL, however, makes sense. Since we have 1 over x on the left side of the equation, we can simply flip both sides to get x on the left… …and one over 3 and a half on the right… which is 1 over 7 halves… or two-sevenths. A it is. As in… “Alien mathletes.”