Main content

## 7th grade foundations (Eureka Math/EngageNY)

### Course: 7th grade foundations (Eureka Math/EngageNY) > Unit 3

Lesson 2: Topic B: Foundations- Equation word problem: super yoga (1 of 2)
- Equation word problem: super yoga (2 of 2)
- One-step equations review
- Writing expressions with variables
- Inequality word problem: one variable
- Inequalities word problems
- Plotting an inequality example
- Plotting inequalities

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Inequality word problem: one variable

This time we're creating a variable to represent a number, and then writing an inequality. We're building on our knowledge. Created by Sal Khan.

## Want to join the conversation?

- Why when the circle is closed does it include the number?(5 votes)
- When the circle is closed it means it includes the number. If you asking why, well i guess that's how its defined.(15 votes)

- the karman line question just lost me(7 votes)
- Hello! We were given this math problem in class but my teacher said it's undefined. We were asked to put either a less than or greater than sign between x 2x

I put < sign because x is the same as 1x and 1x and is less than 2x. Am i wrong?(4 votes) - Isn't the point from when you're not safe called the event horizon(3 votes)
- i want to know what is the definition of and inequality(3 votes)
- when do you know when to use the less than equal to or greater than equal(3 votes)
- At0:40and0:41how did Sal know that c is the Karman line?(2 votes)
- My page does not load on the sections where I have to answer the questions. Every section marked by a star, I am having difficulty loading. Can you help me?(2 votes)
- can you please help me sal khan? i need help(1 vote)

- at about2:00why does it not explain what x and E equal exactly?(2 votes)
- How can you solve this inequality x is less than or equal to 100? Give an example.(3 votes)
- You don't really "solve" inequalities. Inequalities represent a set of allowed values. You can test a value and solve for whether it's true or not. So you could test for x equal to 7, and solving
`x < 100`

for 7 gives`7 < 100`

, which is true. So 7 is included in the inequality for x.(3 votes)

## 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.