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## Linear equations with variables on both sides

# Figuring out missing algebraic step

## 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.