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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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# Solution procedures | Worked example

Sal Khan works through a question on solution procedures from the Praxis Core Math test.

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## Video transcript

- [Instructor] We're asked,
which of the following sequence of steps, when
completed, will solve the equation two X minus
seven is equal to one for X? So pause this video and see
if you can figure it out on your own before we do it together. Okay, so there's two ways
that we can approach it. One way, we can look at
each of these choices and try to follow their directions and see if it gets us solving for X here. Another way to approach
it, which is the way I will approach it to begin
with, is to just start with the equation, two X
minus seven equals one, and then solve for X, or try to do it in the most efficient way that I can. And this is one of the choices, this is one of the questions
where they only want us to pick up one choice, so
once we pick one choice, we know that the other ones
will not be the correct choice. So if I'm going to solve an
algebraic equation like this, the first I try to do is isolate the terms that deal with an X on one side. So to do that, I'd want to get
rid of this negative seven. So the best way I can think
of doing that is to add seven to both sides, so I'm gonna
add seven to the left, and add seven to the right
hand side of the equation. Remember, when we're
dealing with an equation, if we want the equation to hold true, that the left side is
equal to the right side, whatever we do to the
left side, we have to do to the right side as well. So if we add seven on the left, we have to add seven on the right. Well, when we do that, our left side is left with just the
two X, because you have negative seven plus seven, is equal to the right side, is one plus
seven, is equal to eight. Now, how do we solve for X here? Well, we can divide both sides by two, and that will just leave
an X on the left hand side. So when we divide both sides by two, we are left with X is equal to eight divided by two, is four. So what are the steps? First, we added seven to both sides, so let me write this down. So first, we added seven
to both sides, both sides. And then the second step is,
we divided both sides by two. Divided both sides by two. Now, which of these
choices match up to that? So here it says divide
both sides of the equation by two, then subtract
seven from both sides. So this is close, but
they're dividing by two first and then, instead of adding
seven, they're subtracting. And if you divide by two
first, it's not clear that adding or subtracting
seven is the right thing to do. We could even try it out with that, if you divided both sides by two first, if you divide the left hand side by two, you would get two X divided by two is X, minus seven over two is equal to 1/2, when you divide the right side by two, and then you subtract
seven from both sides, that's definitely not
going to solve it for X, we'll rule that out. Divide both sides of the equation by two, then add seven to both sides. So those are the two
steps that we just did, but they're in reverse order, so we can rule that one out as well. Subtract seven from both
sides of the equation, then multiply both sides by two. No, we added seven to
both side of the equation and then we divided both sides by two. Add seven to both sides of the equation, yup that's what we did first, then multiply both sides by two. No, it's going to be then
divide both sides by two. Add seven to both sides of the equation, yup, that's what we did first, then divide both sides by two. That's exactly what we did and that will get you solving for X. They were a little bit tricky here, because the last choice here, so we had to work through all of them to find the one that actually worked.