Express your answer using set notation or interval notation. Graph the solution set. |-x-2| ≥1

Name: Problem 54, Chapter 1: Algebra and Trigonometry
Uploaded: 2020-07-10T14:58:45-08:00
Duration: 4 min 34 s
Channel: Joshua Fischbach
Description: Express your answer using set notation or interval notation. Graph the solution set. |-x-2| ≥1

Express your answer using set notation or interval notation....

Key Concepts

Absolute Value

Absolute value represents the non-negative magnitude of a number, which can be interpreted as its distance from zero. Understanding absolute value is crucial because it transforms expressions into their distance equivalents, irrespective of sign.

Solving Absolute Value Inequalities

This concept involves finding the set of all values that satisfy an inequality containing an absolute value. The typical approach is to split the inequality into two separate cases based on the definition of absolute value and then solve each inequality individually.

Set and Interval Notation

Set notation and interval notation are formal ways to represent solution sets. Set notation uses symbols to describe all elements that satisfy a condition, while interval notation describes all numbers within a certain range, often indicating whether endpoints are included or excluded.

Graphing the Solution Set

Graphing the solution set involves plotting the numbers on a number line, where intervals corresponding to the solution are marked and often closed or open circles are used to indicate whether endpoints are included in the solution.

Transcript

00:01 Okay, when solving the absolute inequality, absolute value of negative x minus 2 is greater than equal to 1.

00:06 The first thing you're going to do is you're going to take out the absolute value bars, and you're going to take the inside, negative x minus 2, and that stays the same.

00:17 So, negative x minus 2, negative x minus 2.

00:22 And there's two possibilities, right? first possibility is that negative x minus 2 is equal to the positive version of that value, which means that everything stays the same and you said it greater than equal to 1.

00:35 The other possibility is that negative x minus 2 is equal to the opposite of that or the negative version of that, which means that we're going to have to change this greater than or equal to to a less than or equal to and change the 1 to a negative 1 because everything that is related to has to be the opposite of the plus.

00:55 And that's it.

00:56 Then you solve it.

00:57 So we want to get the negative x by itself.

01:00 So you add two to both sides in both situations.

01:05 And you're left with negative x is greater than equal to three.

01:10 And over here, you've got negative x is less than are equal to one.

01:14 And then you want to undo times by a negative because you want to have a positive value of x.

01:19 So you can divide by negative one both sides.

01:22 Same thing over here.

01:24 Remember, when you divide by a negative across an inequality, you have to reverse that inequality.

01:29 So what you get here is positive x is not greater than they're equal to, but is less than or equal to, three divided by negative one, negative three.

01:38 Over here, you get positive x is not less than or equal to, but greater than are equal to, and negative one.

01:47 So we're looking at all the values that are less than equal to negative three and greater than equal to negative one, which means that these two are going in opposite directions and they don't have any overlap.

01:58 This is an or relationship, not an an relationship.

02:02 When we graph it, you're going to start with the negative three and make sure that's on your graph and you're going to go let's say negative two say negative one zero you're gonna have closed circles at both negative three and negative one because they are in fact end points so we're gonna have closed circles because of the equals to sign and then you're going to make sure that you shade it appropriately so you're gonna be doing less than or equal to negative three so all the values that are to the left of negative three work so you're going to shade in including the arrow all the values that are less than negative 3 and all the values also that are greater than negative 1 work so you're going to shade to the right there greater than including the arrow now obviously you want to check to make sure this makes intuitive sense so let's think about a value that should work zero should work test it out is 0 minus 2 or the absolute value of negative 2 greater than or equals you 1 the answer is yes 2 is greater than equal to 1.

03:07 Can you also check negative 4 over here? just make sure it works.

03:12 Negative, negative 4 is going to be positive 4...

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