I prefer to always say “reciprocal” because if these couples were livers, then it would be easier to think of them. But in any case, you either multiply by the reciprocal, or divide by the number. 1/2 by 2x is just x, so you get x = -18/2 and -18/2 is just equal to -9. Let’s solve another problem. And if we want to test it, we can simply say that the original task was 2x + 3 = -15. We can say: 2 (-9) + 3. 2 over (-9) is -18, + 3. This is equal to -15, namely, this is what the original equation told us. That is, we know the answer is correct! The good thing about algebra is that you can always check your work. Let’s solve another problem. I’ll take some fractions this time, just to show you that it can get a little more complicated. Let’s say I have -1 / 2x + 3/4 = 5/6. We will do the same thing. First we want to move 3/4 to the left of the equation. If you want to try this on your own, you can now stop the video and play it, when you want to see the answer. Let’s continue. If we want to remove 3/4, we can just subtract 3/4 from both sides. On the left, these 3/4 will simply be destroyed and we get -1 / 2x equal to … On the right we have to do this addition or subtraction of fractions. The least common multiple of 6 and 4 is 12. This happens … 5/6 is 10/12, minus – 3/4 is 9/12 – we get: -1 / 2x = 1/12. I hope I didn’t make a mistake somewhere. If this step confuses you – I did it a little quickly – you can just negotiate the addition and subtraction of fractions. Let’s go back to where we were. Now all we have to do is … the factor in front of x is -1/2, and now this is a level 1 task, so to find x, we just multiply both sides by the reciprocal of -1/2. This is -2/1 and we multiply both sides by it. The left side is simplified to x. The right side becomes -2/12, and we can simplify this to -1/6. Let’s check to be sure of our answer. Let’s try to remember this. We got -1/6 and in the initial task we had -1 / 2x, so we replace with -1/6, + 3/4. I wrote only the left side of the original task. (-1/2) by (-1/6) is +1/12, and then + 3/4. This is the same as 1/12 + 9/12. 1 + 9 is 10, over 12. This is equal to 5/6, which was our initial task. That’s the other thing I wrote later. So the decision is correct. I hope you are ready to solve a level 2 task on your own. I can add some more sample tasks. The only additional step here, compared to level 1 tasks, is that we have this constant that you have to add or subtract from both sides of this equation, and then the task is done from level 1. Have fun! I welcome you to level 2 of “Linear Equations”! Let’s solve a problem! 2x + 3 = -15 I put a minus to make it a little harder. The first thing to do with linear equations is is to transfer all variable terms on one side of the equation, and the constant terms (constants) are on the other side of the equation. I usually put the variables on the left, but it doesn’t really matter. My variable here is already on the left side of the equation, but I also have this “+ 3” that I want to move on the right side somehow. The way we can do it, is by subtracting 3 from both sides of this equation. Think carefully about why this would work. If I subtract 3 from the left side, this initial “+ 3” will be destroyed and become 0. And while I’m doing the same thing on both sides of the equation – what you do on one side, you have to do on the other – the action is correct. This will be simplified to 2x – plus 3 is destroyed, only: 0 = – 15 – 3 remains. This is equal to -18. We are now on a level 1 task. We multiply both sides of the equation by the RECIPROCLE of the coefficient before x. Some say we divide by 2, which is actually what we do.

Algebra