Reasoning with tape diagrams to solve equations
About this video
A tape diagram shows 7(x + 2) = 77 as seven equal parts that total 77. Dividing 77 into seven equal parts shows each part, x + 2, is 11, so x = 9. The video links this to dividing both sides by 7 and then subtracting 2, and checks the answer.
You'll be able to
- use a tape diagram to reason about an equation like 7(x + 2) = 77.
- solve an equation by dividing both sides and then subtracting.
- check a solution by substituting it back.
Key words
- tape diagram
- A drawing of a strip split into parts that shows how amounts add up to a total.
- equal parts
- Pieces that are all the same size.
Transcript
- [Instructor] So we're told the tape diagram represents the equation: seven times x plus two is equal to 77. And what they want us to do is figure out the value of x. So pause this video, have a go at that before we do it together. Okay, since they gave us a tape diagram, actually let's use it to reason through what x might be.
So this whole thing is equal to 77 and it's divided into seven equal parts. We see that here, one, two, three, four, five, six and seven. And that makes sense. If I have seven of these x plus twos, that's the same thing as seven times x plus two. And when you add all those seven x plus twos, it comes up to 77.
Well, these are seven equal parts so each of them, if when I add them up, get to 77, if I divide 77 by seven, each of these, this over here must be 11. This over here must be 11. Each of these must be 11. And so one way to think about it is that x plus two must be equal to 11.
Another way we could have done it if we looked at this, and it's really the same idea, is we're just dividing both sides of this equation by seven. If I divide this side by seven and that side by seven, I end up with x plus two is equal to 11. But that's what we just reasoned through using this tape diagram.
Now, if we know that x plus two is equal to 11, you can say, "Okay, something plus two is equal to 11, that something is going to be nine." Or you could do it a little bit more formally. Yo could say, "Let's subtract two from both sides." And you could say that x is equal to nine.
Either way, we're done. We figured out the value of x. And actually you could test this because if x is nine, then each of these is nine plus two. This is 11, 11, which is our goal. And then if you have seven 11s, seven times 11, you're definitely going to get to 77.
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