If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Lesson 7: Comparing absolute values

# Testing solutions to absolute value inequalities

In this math lesson, we learn how to determine if given values of x satisfy various absolute value inequalities. We examine three different inequalities and test each x value to see if it meets the inequality's conditions. By understanding absolute values and inequalities, we can solve real-world problems and improve our mathematical skills.

## Want to join the conversation?

• I didn't really understand anything after . Could you explain that better?
• absolute value is like size, or distance. Saying you have a shoe size of 11 makes sense. Saying that you have shoe size negative 10 makes no sense. So absolute value is like size. For it to make sense it is always positive. So absolute value of anything is positive. So any x that you take absolute value of becomes a positive size and is always greater than any negative because even the very small positive numbers like say +.00000000001 is greater than any negative number. So |x| > -16 is true for any x. So you don't need to check any values because |x| is always > -16.
• dang, people have not commented on this video for literal years bro🥹
• For real tho-
• I forgot that I changed the speed of the video so now he's just talking incoherent words.💀
• at ~ sal says that the absolute value is going to be greater than -16 but wouldn't -16 be = to 16 because it is absolute value?
• |𝑥| > −16
This means that we have some number 𝑥 which we take the absolute value of and then we compare it to (−16), and since the absolute value of 𝑥 will never be negative the inequality
|𝑥| > −16 will always be true regardless of what 𝑥 is.

If the inequality had read |𝑥| > |−16|, then we could simplify to |𝑥| > 16
• Sal I didn't understand a thing 😔😞😞
• Hey I may not be Sal but its a really simple lesson. And I could help you if your more specific. (oh screw me im late by 5 years!)
• if i have a negative answer, i have to multipliy by-1 for the absolute answer?
• Yes, or you could divide by negative one, and that would give you the correct answer too.
• Will it always tell you what x equals?
• No. In that case, you will just simplify it as much as you can
• In the video, you state that an absolute value is the distance away from zero on a number line. Is this the same as the idea of displacement in physics?
• Questions
At , why does Sal X out the problems?
Do they cancel out or what?

`Appreciate all answerers and commenters.`