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### Course: Algebra (all content) > Unit 2

Lesson 13: Introduction to inequalities with variables# Inequalities word problems

Inequalities are a handy tool for comparing values. For example, if Eric is shorter than Priti who is 158 cm tall, we write E < 158. If Sydney wears skirts when it's warmer than 25 degrees, we say T > 25. If Hayley finishes a race after Lola's 53 seconds, we write H > 53.

## Want to join the conversation?

- can the variable be on either side and if not how does that change it?(23 votes)
- The variable can start out on one or both sides. When you finish solving, the variable will be on one side. It does not matter which side. For example: x>3 is the same as 3<x

Hope this helps.(14 votes)

- How about if you have a problem like this? :

Describe the numbers x and y such that if x>y, then x^2=y^2

I tried to write an equation like this:

x>y=y^2

This is as close as I have gotten so far. If someone could explain the procedures to do this problem, that would be greatly appreciated! Thank you! :)(17 votes)- x=-y should be the answer. For example, if x is 2 and y is -2, x^2=y^2=4. Hope this helps.(5 votes)

- What are ways to check inequalites(5 votes)
- Can you explain what you mean by "Checking" inequalities? Do you want to compare them?(6 votes)

- I dont know how to do the inequality test it is hard for me I cant do the plotting nor the graphic(4 votes)
- Why is this so hard?(2 votes)
- Because it´s math(4 votes)

- Haleys time would be after 53 since that Haleys time was less than 53 seconds so the inequality would be written(2 votes)
- If you are trying to say that Haley's time should be reflected as: H < 53 (so, less than 53), that is incorrect. Lola finished in 53 seconds. Haley finished
**after**Lola, so her time must be more than 53. Thus the inequality shown in the video is correct: H > 53(4 votes)

- easy i just thought that o was weird(3 votes)
- The temperature every day for a week was above 70 degrees. Write an inequality for the situation, use x as the variable.(2 votes)
- How do I know if an equation is an all real number?(2 votes)
- thought about monkey(2 votes)
- i think they are great(1 vote)

## Video transcript

- [Instructor] We're told that Eric is shorter than Priti. Priti is 158 centimeters tall. Write an inequality that
compares Eric's height in centimeters, E, to Priti's height. Pause this video and
see if you can do that. Alright, so we have Eric's height, which we are using the
variable capital E for, And how does it compare? It says Eric is shorter than Priti. So Eric's height is going to be less than whatever Priti's height is,
which is 158 centimeters. You could think about
it on a number line too. If I were to draw a number line like this, and this is 158
centimeters, Priti's height, Eric's is gonna be less than
that 'cause he is shorter. So it would be all of the
values that are to the left of, let me do this in another color, that are less than that. Just like that. Let's do another example. Here we are told that Sydney wears skirts when the temperature is warmer
than 25 degrees Celsius. Write an inequality that describes T, the temperatures at which
Sydney wears skirts. So again, pause this video and see if you can have a go at that. Alright. So when does Sydney wear skirts? When the temperature is warmer
than 25 degrees Celsius. Now, warmer means that
the temperature is higher than 25 degrees Celsius, or that the temperature is
greater than 25 degrees Celsius. And we're using capital
T to denote temperature. So we would say capital
T, this needs to be higher than 25 degrees, or greater
than 25 degrees Celsius. So T is greater than 25. Let's do one last example here. So here we are told that Lola
and Hayley are running a race. Lola finishes the race in 53 seconds. Hayley finishes after Lola. Write an inequality that represents H, Hayley's finish time in seconds. Pause the video and see if
you can think about this. Alright, so how does
Hayley compare to Lola? Hayley finishes after Lola. So what does that mean
about Hayley's time? Well, that means that Hayley
is going to take more time than Lola to finish the race. So whatever Lola's time is, Hayley's time is going to be longer,
or more, or greater than. So Hayley's time is going to
be greater than Lola's time, which is 53 seconds, because Hayley finishes after.