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## Arithmetic (all content)

### Course: Arithmetic (all content) > Unit 4

Lesson 3: Absolute value- Absolute value examples
- Intro to absolute value
- Finding absolute values
- Identify and order absolute values
- Comparing absolute values
- Placing absolute values on the number line
- Compare and order absolute values
- Absolute value as distance between numbers
- Absolute value to find distance
- Absolute value word problems
- Absolute value review

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# Absolute value word problems

Learn to solve word problems that ask us to apply our new absolute value knowledge. Created by Sal Khan.

## Want to join the conversation?

- Is there a term for the little lines indicating absolute value?(39 votes)
- The two lines on either side of a number indicating the absolute value are called
**vertical bars**.(33 votes)

- Is absolute value supposed to be easy if not it seems really easy because I can even do it and i get confused when i see negative and positive numbers for absolute value?(11 votes)
- It's a pretty simple skill in my opinion.

The absolute value of negative and positive numbers will always be positive.

Examples:

Absolute value of -5 = 5

Absolute value of 5 = 5(6 votes)

- All of these absolute value tutorials are terrific. However, I still have no idea why one would learn this or, in other words, how does this apply to life or even upcoming math?(7 votes)
- Well, you could apply this to distance of two things from an object where west of that object(which means the object is 0) is negative and east of that object is positive. Also, you could apply this where sea level is 0 and being underwater is negative while flying is positive. Hope this helps!(15 votes)

- What does the absolute value mean?(4 votes)
- I've watched this video at least five times now, but I still don't understand how to do the problems that say, for example,:5>x |x|>|5| What is a possible value for x?(3 votes)
- Meh name is jeff i like turtles and u need some milk!(1 vote)

- Is absolute value always positive?(2 votes)
- Absolute value just measures how far away a value is from 0. We can't measure distance in negative units, so it will always be positive.(2 votes)

- Well, the simple answer is that the absolute value of a number simply is the positive form of the number.

|98| = 98

|-17362| = 17362

|-pi| = pi

That's the easiest way. Just get rid of the negative sign and boom, you've done the absolute value. But that's not really the point. What does absolute value actually mean?

Absolute value is a number's distance from 0. Since we can't really have negative distances, this explains why absolute value always is positive. So how far from 0 is 98? Well, it's 98 units away, so it's 98. How far is -67 from 0? Well, it's 67 units from 0 since we can't have a negative distance, so it just yields 67.

Does this make sense? Reply if you need further clarification.(2 votes) - I am attempting the Absolute Value Word Problems and i need some help with these types of questions.

We want the two following inequalities to be true for the same value of x:

x>0.5

|0.5|>|x|

What is a possible value for x?

What are you asking for? Is it a number that would make both of these statements true when a certain number/s were applied to x?(2 votes) - Hi, I have math exam next week. i have watched the Absolute value video , but it did not answer my question which is:

the problem was: what is the sum of the solutions to the equation /x-3/ = 7 ?

the Choices were: -4 , -6 , 6 , 10 , 0

I Scrupled between -4 and 10 because the solution for both of them will be correct, but i had to choose only one. i chose -4, but it was incorrect.

why pleas?

the same problem with /x-7/=6

10, -10, 11, -1, 0

i chose 11, but also it was incorrect.

why -1?(2 votes) - The absolute value it is allways positive,right(2 votes)
- Yes, the absolute value is always positive.(1 vote)

## Video transcript

The Statue of Liberty,
pictured above, is a gigantic sculpture
located on Liberty Island in New York, United States. The height of the
sculpture is 151 feet. So this distance right
over here is 151 feet. So it's like a 15 story
building or more, or about a 15 story building. The distance from the
ground to the torch is 305. So from here to
there is 305 feet. What is the absolute
value of the difference between 305 and 151? Well we just have to
subtract 151 from 305. And you might be able
to do that on your head. Let's see, if you add 150
to 151, you get to 301. So then you have to add
another 4, so it's 154. Or you could use a
calculator right over here. You could say 305 minus
151 is equal to 154, which is what we
did in our head. And the absolute
value of 154-- there's a couple of ways you
can think about it. You could learn to
just view it as, how far is that number from 0? And positive 154
is 154 away from 0. If this was negative
154 then that also would be 154 away from 0. The other way to
think about it is, whether it's
positive or negative, the absolute value,
you just take the positive version of it. So either way we say 154. Let's do a couple more of these. I like these pictures. The average weight of a
car in the United States is roughly 4,000 pounds. The dinosaur Ankylosaurus--
artist rendering above-- is thought to have weighed
up to 13,000 pounds. What is the absolute
value of the difference between these two weights? And you could calculate the
difference between these two weights. You could take the smaller
and subtract from the larger. So if you take
4,000 from 13,000, the difference would
be 9,000 pounds. The absolute value
of 9,000 is 9,000. You could have
gone the other way. You could've subtracted
13,000 from 4,000, and you would have
gotten negative 9,000. But the absolute value of
negative 9,000 is still 9,000. So we just want to think
about the absolute difference between these two. We don't want to
think about which one we're subtracting
from whichever one. Whatever we're subtracting
from the other one, we just find the
absolute difference. So whether the difference
was negative 9,000 or 9,000, depending on which one you
subtract from the other, the absolute value
of either of those is going to be 9,000 pounds. Let's do one more. No picture this time. I was getting used to that. The Panama Canal
is a canal cutting through the country of Panama
that conveniently connects the Atlantic and Pacific Oceans. What's nice about
these is we learn other things other
than mathematics here. France began constructing
the canal in the year 1881 and, after the French
abandoned construction, the United States finished
construction in 1914. What is the absolute value of
the difference between the year construction of the
Panama Canal started and the year that it ended? Well, there's a couple
ways you could do it. You could take the larger year
and subtract the smaller year from it. We have our calculator here. You could literally
say 1914 minus 1881, and you get 33 years. And the absolute value
of 33 is just 33. Or you could've done it
the other way around. Since we're taking
absolute value, it doesn't matter what we
subtract from the other ones. You could do on 1881
minus 1914, and you would've gotten negative 33. But the absolute value of
either of these numbers is, you're saying, how far
is 33 or negative 33 from 0? Well, they're both
33 away from zero. Or you could say, well, what's
the positive version of either of these? Well, it's 33. So the absolute value of
the difference in the years is 33 years. And we're done.