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Danielle said that there is no integer that makes the inequality $|2 x+1|<x$ true. Do you agree with Danielle? Explain your answer.

Yes

Algebra

Chapter 1

THE INTEGERS

Section 3

Adding Polynomials

The Integers

Equations and Inequalities

Polynomials

Oregon State University

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

04:15

Maria said that since the …

02:40

Error Analysis Your friend…

00:52

True or False The inequali…

00:18

True or False The absolute…

00:54

Explain why the inequality…

00:30

List or describe the integ…

01:54

Solve the inequality $\lef…

00:44

the set of real numbers sa…

01:16

00:35

A student solved the inequ…

Hey, guys. So in this problem, we were given the point of view of another student. Her name is Maria, and Maria says that if you have the absolute value of two X minus five is less than three, then the solution to this is gonna be the same as the solution of this compound. Inequality negative three Less than to explain A spy is less than three. Now let's just check if this correct. If Maria's correct, explain why and why not. So when you have the absolute value equations up so value to X minus five less than three you can write that as two separate inequalities. You can write that as two X minus five is less than three, and you can also write that as two X minus five is greater, then minus three. For this is the same thing as saying, minus three is less than two X minus five and one key crucial step inequality trick. Kind of the definition, in a sense, is if you have a is less than be and B is less than C, you can rewrite. This is a less than be less than see, and that means therefore that's a symbol for therefore, A is also less than see. This has to be true if we want to write this inequality out like this. And so in this case, we have to x minus five is less than three. Minus three is less than two x minus five. So when we write, minus three is less than two. X minus five is less than three in order to check if this is true, is if we check our A N C value or negative three and three, we see net negative. Three is less than three. So this compound inequality, the way it's set up, is correct. Maria is correct that this absolute value inequality can be rewritten as this. She's correct in this terms, so let's take a look at another inequality she says she talks about. She says that I absolutely have to minus five is greater than three. She implies that my which implies that according to me, according to Maria, she says that this implies that minus three is greater than two. X minus five is greater than three Now, right off the bat, we see something that's wrong with this. We see that minus three is greater than three now that's already a big no no. That can never happen, because negative number is never greater than a positive number. The way that Maria wrote this is incorrect. Now let's let's go to the steps, though, unless we know that two X minus five is if you split this inequality into two. We know that two X minus five is great and threes are first inequality, and we know that two X minus five is a less than minus. Threes are second in the quality. Now, if you write this in terms of just algebra values, this basically boils down to a greater than be and a is less than see now just cause you know that is greater than something. And AIDS less than something doesn't mean you know any explicit things about the values B and C, and as a result, you don't know the relationship between being see from these given expressions. And so as a result, you can't make a compound inequality out of these expressions. And as a result, this is just another way of explaining why Maria is incorrect. This way is more clearly defined because we see that minus three can never be greater than three. That's gonna be incorrect. So just to recap, Maria was correct when she said that when you had two x minus by absolute value to X minus five less than three. That's equal to this expression. She is totally correct in with regards to this expression. And she's totally incorrect with regards to this expression. Reasoning why she's incorrect is that minus three could never be greater than three. Thanks for listening, guys. I hope this help with the intuition behind. Why about

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