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## Praxis Core Math

### Unit 1: Lesson 4

Algebra- Algebraic properties | Lesson
- Algebraic properties | Worked example
- Solution procedures | Lesson
- Solution procedures | Worked example
- Equivalent expressions | Lesson
- Equivalent expressions | Worked example
- Creating expressions and equations | Lesson
- Creating expressions and equations | Worked example
- Algebraic word problems | Lesson
- Algebraic word problems | Worked example
- Linear equations | Lesson
- Linear equations | Worked example
- Quadratic equations | Lesson
- Quadratic equations | Worked example

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# Equivalent expressions | Worked example

Sal Khan works through a question about equivalent expressions from the Praxis Core Math test.

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- wow thanks sal, this helped so much(1 vote)
- what does the x and y mean in the equation can you basically choose your expression?(1 vote)

## Video transcript

- [Instructor] Which of
the following expressions are equivalent to three x
minus 20 for all values of x, and it says choose all answers that apply and they give us three choices. So like always, pause this video and see if you can work through it on your own before we
work through it together. All right, now the way that I
would approach this is I would try to manipulate these expressions, and see if I can make it
equivalent to this expression. Another way that you could do it that might involve a
little bit less algebra is to just try out values for x, and see what three x minus
20 would be equal to, and try out these values. Now, that might be a
little bit more spotty, depends on what values you pick. So let me do it the first way, and then we could do it the
second way if you're interested. It's not as robust. So the first way is
let's just rewrite this and try to write it in this form. So I would first try to distribute the three over the x minus seven, so that's going to be
equal to three times x, which is three x, minus three times seven, which is minus 21. So all I did is I distributed the three on the x minus seven, and
that's three x minus 21, and then we have plus one. Now, what is negative 21 plus one? Well, that's going to be equal
to negative 20, so this is going to be equal to
three x minus 20, right, which is exactly what we originally had. And since we did it algebraically, we know that it works for all values of x, so we like this choice. Now let's look at this one. So once again, we would probably want to start by distributing the three, so three times x plus one, then minus 23, this is going to be the same thing as three
times x plus three times one, so plus three, and then we're going to subtract 23, minus 23. Now, what is three minus 23? Well, once again, we have to make sure that we're doing arithmetic with our negative numbers appropriately, but this is going to be negative 20. So this is once again going
to be three x minus 20. Looks correct again,
so I like that choice. Now let's try this one. So here, we have seven and then we have three times this expression, so we can distribute the three here. So this is going to be
equal to seven plus, and then three times x, I'm just distributing the three now, minus three times nine, so minus three times nine
is 27, and so let's see, I can rearrange these,
so I could rewrite it as, this is the same thing as
three x minus 27 plus seven. Now, what's negative 27 plus seven? Well, that once again is going to be negative 20,
so this whole thing is going to be equal to three x minus 20. So actually, all of these answers apply. Now, another way that you
could've done it as I mentioned that might be, that actually
would be less robust, is to just try out values. So you said, okay, let
me just see what happens when x is equal to one. So if x equal to one, then this one right over here would
be three times one minus 20, which would be negative
17, and then over here, you would have three
times one minus seven, so that would be negative six, and then three times negative six is negative 18, plus one
would be negative 17, so that would actually look
pretty good for just the case of x equals one, but once again, that wouldn't necessarily make
you feel good for all x's, and you would be able to do
the same thing with choice b and c, and you would
get back to negative 17, but once again, this method
is not as robust as just being able to algebraically
manipulate these choices and see if you can make them
equivalent to three x minus 20.