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# Inequality word problem: one variable

## Video 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.