Inequality word problem: one variable
About this video
Sal writes one-variable inequalities from two word problems. Distances inside Earth's atmosphere are below the Karman line, so x < c, and safe distances from a black hole are farther than E, so x > E. In both cases he reads carefully to decide whether the boundary itself is included, choosing a strict inequality.
You'll be able to
- write an inequality from a word problem using a variable and a given value.
- decide whether a boundary value is included and choose < or ≤ (or > or ≥).
- explain what an inequality means in the context of the problem.
Key words
- inequality
- A math statement that compares two values using signs like <, >, ≤ or ≥.
- Karman line
- The height, 62 miles above sea level, where Earth's atmosphere ends and outer space begins.
- strictly less than
- Smaller than a value but not equal to it, written with the sign <.
- black hole
- A region of space where gravity is so strong that nothing can get back out once it falls inside.
Transcript
The Karman line is the point at which the Earth's atmosphere ends and outer space begins. The Karman line is at 62 miles above sea level. And any distance from sea level at the Karman line or above is considered outer space. Set c equals 62 and use x to represent distance from sea level.
Write an inequality in terms of x and c that represents the distances from sea level that are inside Earth's atmosphere. So we want to write an inequality in terms of x and c. And x is the distance above sea level, and c is the Karman line. And we want to think about things-- we want to think about distances that are inside Earth's atmosphere.
So that's going to be anything that's below the Karman line. And so, let's see, I would write x is less than c, because they're telling us c is 62. Now, I want to make sure. So they say the Karman line is the point at which the Earth's atmosphere ends and outer space begins.
So what if we're right at 62 miles? The Karman line is 62 miles above sea level, and any distance from sea level at the Karman line or above is considered outer space. OK. So if I'm at c or above, I'm in outer space. So only the things that are not, I'm sure, they're strictly below c.
So I'm going to do a less than, not a less than or equal sign right over here. All right, got it right. Let's do another one. A black hole is a region of space where the pull of gravity is so strong that nothing can get back out once it has fallen inside. Let's use E to represent the largest distance from the center of the black hole that pulls objects inside.
If x represents the distance of an object from the center of the black hole, write an inequality for safe distances from the center of the black hole in terms of x and E. So x is the distance from the center. e represents the largest distance from the center of the black hole that pulls objects inside.
So if you're at E away or closer, you're going to be pulled inside. But we want to think about safe distances. So if you're further away than E, you should be cool. And it's strictly greater than because if you're at E, that's the largest distance that you would still be pulled inside.
Very good.
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