Writing inequalities to represent problems
About this video
Triangle PQR has sides PQ = 2.9x + 8, PR = 4.6x - 3 and QR = 10x, and the sum of PQ and PR is greater than QR. Sal writes the inequality (2.9x + 8) + (4.6x - 3) > 10x, explains the notation for a segment's length, and simplifies it to 7.5x + 5 > 10x.
You'll be able to
- translate a word statement about lengths into an inequality.
- tell the difference between a segment and its length in notation.
- simplify an inequality by combining like terms.
Key words
- inequality
- A maths statement that compares two amounts using symbols like > or <.
- segment
- A straight piece of a line between two points, like PQ.
- length of a segment
- How long a segment is, written as PQ without a bar on top.
- like terms
- Terms with the same variable part, like 2.9x and 4.6x, that can be combined.
Transcript
- [Instructor] We're told triangle PQR is shown with the dimensions given in units. So 2.9X plus eight is the length of that side. 4.6X minus three is the length of that side. And then 10X is the length of segment QR. The sum of the lengths of segment PQ and segment PR is greater than the length of segment QR.
Write an inequality that represents this situation. So Pause this video and have a go at it before we do it together. Alright, now let's do this together. So first of all, they say the sum of the lengths of segment PQ and PR. So you could write the length of segment PQ as just writing it as PQ, like that.
And then you add that to the length of segment PR, which we could just write as PR. The geometric notation if you put the line on top of it like that, you're talking about a lot. You're talking about you're representing the actual line segment. If you don't put that line segment on top, then you're representing the length itself.
So the length of segment PQ plus the length of segment PR, they say it's greater than, greater than the length of segment QR. So it's greater than the length of segment QR. And they've told us that PQ, the length of segment PQ is right over here. That is 2.9X plus eight.
So lemme write that 2.9X plus eight, and then the length of segment PR, that's that right over here is 4.6X minus three. So plus 4.6X minus three. That is going to all be greater than the length of segment QR, which they told us is 10X. And we're done. We've written an inequality that represents this situation.
Now, if we wanted to simplify it a little bit, we could, let me scroll down a little bit. We could add the 2.9X to the 4.6X and where does that get us? That gets us to what? 7.5X. 7.5X and then if you combine the eight and the negative three plus five is going to be greater than 10X.
So the one I just wrote is a little bit simpler, but what I had before is also an equality that represents an inequality, I should say, that represents this situation.
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