Modeling two step inequalities
About this video
The video solves the inequality 3T - 1 ≥ -16 using blocks. Adding 1 to both sides cancels the -1 and leaves 3T ≥ -15, then splitting both sides into three equal groups shows T ≥ -5.
You'll be able to
- model a two-step inequality with blocks.
- solve a two-step inequality by doing the same thing to both sides.
- explain what a solution like T ≥ -5 means.
Key words
- inequality
- A statement that compares two amounts using signs like ≥, ≤, > or <.
- greater than or equal to (≥)
- The left side is bigger than or the same as the right side.
- constant
- A number on its own, like -1 or -16.
Transcript
- [Instructor] What we're gonna do in this video is try to simplify or think about the solutions to this inequality right over here, but we're going to do it visually. So we've represented it two ways. This is an algebraic inequality. 3T minus 1 is greater than or equal to negative 16.
And this is just another way to represent it. I have 3 Ts and I have a minus 1 or a negative 1, and that's greater than or equal to. And you could see that I have 16 negative 1s right over here. So that's equivalent to negative 16. So let's think about how we would approach this.
Well, what I like to do is get rid of all of the other constants on the same side as my variable. So I wanna get rid of this negative 1 on the left hand side. And the best way that I can think of doing that is to add 1, but I can't just do it to one side. I have to do it to both sides.
I'm going to add 1 to both sides. And if I wanna show that here, I will have a positive 1 there and I could have a, let's say a positive 1 right over here. Well what's that going to do? Well on my left hand side, the negative 1 and the positive 1 cancel out. That and that cancel out.
And so all I'm left with is this 3T on the left hand side. We'll do that same color. All I'm left with is that 3T and then that's going to be greater than or equal to. On the right hand side we see that this positive 1 and at least one of the negative 1s, and to say that one right over there, lemme do that in a color that you can actually see.
And that one right over there, those two will cancel out. And so you are left with negative 15. And actually let me really remove them to make it much simpler to look at. So those two are gone, they canceled out each other, and then these two are gone. They cancel out each other.
So the next thing that we're gonna wanna do if we're trying to solve for T, is well we could say if 3T is greater than or equal to negative 15, let's divide both sides by 3. Let's divide both sides by 3. And you could view that as three equal groups. So on the left hand side, three equal groups of T.
And on the right hand side, if I wanted to do three equal groups, I could have, let's see, I could do one group, I think I could do three equal groups of negative 5. So that's my second equal group of negative 5. And this is my third equal group of negative 5.
So those are three equal groups. Each of them are of negative 5. So we could say here that T, same color, T is greater than or equal to negative 5. And you see that algebraically too. 3T divided by 3, it's just T. Negative 15 divided by 3 is negative 5.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.