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the Karman line is the point at which the Earth's atmosphere ends in 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 or its 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 a C is 62 now I want to make sure so they say the carbon 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 common line is 62 miles above sea level and any distance from sea level at the Karman line or above is considered outer space okay so if I'm at sea or above I'm in outer space so only the things that are not material are 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 is 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 close you're going to be pulled inside but we want to think about safe distances so if your further away then II 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