Main content

## Topic B: Foundations

# 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.