About this video
The video solves the two-step equation 17 = 8 - 5t by subtracting 8 from both sides and then dividing both sides by -5, giving t = -9/5. It then graphs -9/5 on a number line, showing it is the same as -1 4/5, just to the right of -2.
You'll be able to
- solve a two-step equation by doing the same operation to both sides.
- divide by a negative coefficient to isolate a variable.
- locate a negative fraction like -9/5 on a number line.
Key words
- two-step equation
- An equation that takes two inverse operations to get the variable by itself.
- constant
- A number on its own that doesn't change, like the 8 or the 17.
- isolate
- Get the variable alone on one side of the equation.
- number line
- A line with numbers placed in order, used to show where a number sits.
Transcript
- [Instructor] What we're gonna do in this video is solve this equation here and then graph the solution on a number line. So let's start by thinking about how we would approach this and pause this video and see if you could have a go at it on your own before we do this together.
Alright, so the way my brain likes to do it is I like to get all the things that involve T like we have this, I guess you could view it as a negative five T over here, or subtracting five T. Let's get that on one side and to get all the other constants on the other side.
So one way to do that is to get rid of this eight. A way to get rid of the eight is to subtract an eight from the right hand side. But if you want the left and the right to still be equal, whatever you do to the right, you have to do to the left or vice versa.
So we have to subtract an eight from both sides. And so what do we get? Well, the left hand side, 17 minus eight is nine. That's going to be equal to negative five T because these right over here cancel out with each other. So that is negative five T. And so the next thing that I would want to do is I wanna just have a pure T on the right hand side.
And one way to do that is if I were to divide the right hand side by negative five, 'cause negative five T divided by negative five would just be T. But once again, I can't just do that to one side. Whatever I do to the right hand side, I have to do to the left, and vice versa.
And so now I get that T is equal to nine divided by negative five, which is the same thing as negative nine fifths. So now let's graph this on the number line. And the whole value of doing that is just to really appreciate where this number sits. So let me draw a number line like this and then let me, it's a negative number so I wanna make sure I have enough space for that.
So, and I can think about this, negative 10 fifths would be the same thing as negative two. So this is almost negative two. So lemme draw it this way. This is negative two, maybe this is negative one, and then this is zero. I could keep going positive if I want, and I could put this, I could split these up into fifths to make it even a little bit clearer.
So I'm not gonna do it perfectly when I do it by hand, but it'll be something like that. One, two, three, four, five. And so this number, negative nine fifths, that we've solved for T, that would be right over here. It's the same thing as negative one and four fifths.
So that's this point right over there on the number line. And we're done.
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