Linear equations | Worked example

- [Instructor] We are told, if negative two times the expression seven X minus four is equal to seven times the expression X minus one, what is the value of X? So pause this video and try to work through it on your own. All right, we will now do it together and there's two ways to approach it. You could just try to solve this equation for X, or you could try to substitute these values and see which of these hold true over here. Now, I definitely suggest the former, because substituting these values actually gets quite hairy, and you would have to do it five times so let's just try to solve for X. So I'm just going to rewrite the equation. I feel that just helps me digest things better. Is equal to seven times X minus one. Now we wanna get to a situation where all of our X terms are on the left-hand side, or on one side, usually the left, and all of our constant terms, or non X terms, are on the right-hand side. But to even start to do that, we first have to simplify these expressions on the left and the right and the most obvious way to do that is to distribute the negative two onto this expression. So it's going to be negative two times seven X is negative 14 X, and then negative two times negative four, make sure to pay attention to those signs, negative two times negative four is positive eight and that's going to be equal too. We now distribute the seven onto the X minus one. Seven times X is seven X. Seven times negative one is negative seven. Now we can try to rearrange things so our X terms, let's try to get them on the left-hand side. So we'd wanna leave this negative 14 X here but we wanna get rid of this seven X. So what we can do is we can subtract seven X from the right but of course if we want to subtract seven X from the right we have to it from the left, as well, if we want to keep this being an equation. Keep this equality here. Whatever we do to the right, we have to do to the left and vice versa. And so this is going to get us to our left-hand side, negative 14 X plus negative seven X. Well that is negative 21 X. Negative 21 X plus eight is equal to, these cancel out, and then equal to negative seven. And now we want to get rid of this positive eight on the left-hand side. Well we can subtract eight from the left. But if we do that we have to subtract eight from the right, as well. And so this is going to give us, on the left-hand side we have negative 21 X. These cancel out. That's equal to negative seven plus negative eight is negative 15. So now all of our X terms are on the left-hand side, and it's fairly simplified or very simplified, and all of our constants on the right. Now to solve for X, we just have to divide both sides by the coefficient on X. So we can divide both sides by negative 21, by negative 21, and we are going to be left with X is equal to. Now if you divide a negative by a negative you're going to get a positive. So this is the same thing as 15/21 but we can rewrite this expression especially because we're not seeing 15/21 here. Now if we think about a common factor 15 and 21, three might jump out at you. So if you divide both the numerator and the denominator by three, you're going to get, 15 divided by three is five. 21 divided by three is seven. So X is equal to 5/7 which is this choice right over there.