In this video, we're going to cover how to do questions like these, where you have to rearrange formulas to get a particular letter by itself. To do these questions, you do basically the same thing as when you solve equations. So you just rearrange the formula until you get the letter that you've been asked to find all by itself. In this first question on the left, they are asking us to make x the subject. So we need to end up with just an x on the left hand side equals something on the right.
To do this we first of all want to get the x by itself by getting rid of this 4 and this 3. So to get rid of the 4 we take our equation and just subtract 4 from both sides giving us y-4 equals 3x. And to get rid of the 3 we just divide both sides by 3. but importantly it's the whole of the y minus 4 that we're dividing by 3, and that will equal a single x. The more common way to write this though is to show the division using a fraction line with a 3 on the bottom, which still means divided by 3, but this way you don't need to bother with the brackets, and again we'll still have x on the right. Then the very last thing we need to do is swap the two sides around to write it as x equals y minus 4 over 3, so that our x is on the left and counts as a subject of the equation. For this second question you need to get the b by itself.
So first you need to get rid of the minus 5 by adding 5 to both sides, so that you get a plus 5 equals b over 3. Next you need to get rid of the divided by 3 fraction. by multiplying both sides by 3. But just like in the last question, this means that you have to multiply everything on the left hand side by 3. So you can put the a plus 5 in a bracket, and multiply the whole thing by 3, which you can then expand to 3a plus 15 equals b. And lastly we just swap it around to get b equals 3a plus 15. Let's try a couple more. For this first one, the x that we're trying to get by itself is inside a bracket.
So the first thing we need to do is expand the bracket by multiplying the 3 by the 2 and the x, giving us 2y equals 6 plus 3x. Next, we need to get rid of the 6 by subtracting 6 from both sides to get 2y minus 6 equals 3x. And then we can divide both sides by 3 to get 2y-6 all over 3 equals x, which we can then swap around to get x equals 2y-6 all over 3 as our final answer.
For the last question, the first thing we do is subtract 3 from both sides to get 6a-3 equals b over 2. Then to get b by itself, you just multiply both sides by 2. And again it'll be the whole 6a-3 that you need to multiply by the 2. So you can expand the bracket by multiplying the 2 by 6a to get 12a, and by minus 3 to get minus 6, which will all equal b. So our final answer will be b equals 12a minus 6. Anyways, that's everything for this video. So if you found it useful, then please do give us a like and subscribe.
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