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Figuring out missing algebraic step

There is a hidden step in Steven's solution to solving an equation. There are different ways to solve an equation. To find Steven's missing step, we can see what we would do in the equation. Then we can see if another step will get us to the work Sten is showing. If not, we can try solving a different way. Created by Sal Khan.

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Video transcript

Voiceover:Below are the steps that Steven used to correctly solve the equation six X is equal to three times X plus four, four X. Step one is missing. What could Steven have written for step one? So let's see, so this is the original equation, they give us a blank for step one, and then we see that he eventually gets to three X equals 12. That he divides both sides by three and he gets to X equals four. So the best way I could think about doing this is to think, what would I do? Well if I saw something like this, my extinct would be to distribute this three so that I could start separating the parts of this expression that have a variable, that have the X, and the parts that are constant. So let's try to distribute this three and see what we get. and see if that's a reasonable step for the direction that Steven went in. So if we do that, we'd get six X is equal to, we haven't changed the left-hand side, and the right-hand side three times X is three X. Then three times four is 12. So you get six X is equal to three X plus 12. Now if I don't even look at what Steven's doing right over here, if I'm trying to solve for X, what would be the next thing that I would do? Well, I'd try to isolate all of the X's on one side, and if I want all the X's on the left-hand side I would subtract three X from both sides. So if you subtract three X from both sides you would then get Steven's second step right over here. So this looks like a completely reasonable first step for Steven. The first step is he distributes the three to get this expression, then he subtracts three X from both sides to get three X is equal to 12, and then he divides both sides by three to get X is equal to four.