Figuring out missing algebraic step
About this video
Sal works out the missing first step in Steven's solution of 6x = 3(x + 4). Distributing the 3 gives 6x = 3x + 12; then subtracting 3x from both sides gives 3x = 12, and dividing by 3 gives x = 4.
You'll be able to
- use the distributive property to remove brackets in an equation.
- collect the variable terms on one side by subtracting from both sides.
- figure out a missing step by working forwards and checking against the next step.
Key words
- distribute
- Multiply the number outside the brackets by each term inside, e.g. 3(x + 4) = 3x + 12.
- constant
- A term with no variable, like 12.
- isolate
- Get all the variable terms by themselves on one side.
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.
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