Graph and Solve 4-2x>8 & 4-2x<0: Interval Notation (-2,2)

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Homework Help Overview

The discussion revolves around solving the inequalities involving the expression |4-2x|, specifically |4-2x| > 8 and |4-2x| < 0. Participants are exploring the implications of these inequalities and their graphical representation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the necessity of considering the cases 4-2x > 0 and 4-2x < 0, questioning whether these steps are required given the original problem statement. There is also a focus on the interpretation of the inequalities and the correct application of mathematical rules, such as reversing inequalities when dividing by negative numbers.

Discussion Status

The discussion is active, with participants providing different interpretations and approaches to the problem. Some have suggested that the original poster's answer may not be valid, prompting further examination of the inequalities involved. There is no clear consensus, but various lines of reasoning are being explored.

Contextual Notes

Participants are navigating the complexities of absolute value inequalities and their graphical implications, with some expressing uncertainty about the classification of the thread within the forum's categories.

elmosworld403
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l 4-2x l >8
4-2x>0 4-2x>8
-2x>-4 -2x>4
x>2 x>-2

4-2x<0 4-2x<8
-2x<-4 -2x<4
X<2 X<-2

-2< X < 2

ANSWER- (-2,2) interval notation

Do I have to keep doing the 4-2x>0 4-2x<0 Even tho it doesn't say it in the question?
It is also asking me to graph it, just graph it on a number line?
 
Last edited:
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elmosworld403 said:
l 4-2x l >8



4-2x>0 4-2x>8
-2x>-4 -2x>4
x>2 x>-2

4-2x<0 4-2x<8
-2x<-4 -2x<4
X<2 X<-2




-2< X < 2

ANSWER- (-2,2)

Do I have to keep doing the 4-2x>0 4-2x<0 Even tho it doesn't say it in the question?
You can see that the answer can't be (-2,2) by taking a number in that interval such as 0 and noticing that it doesn't satisfy the inequality.

I'm not sure why you wrote 4 - 2x > 0 and 4 - 2x < 0. These are mutually exclusive (they can't both be true), and in any case neither one of them follows from the original inequality.

|4-2x| > 8 means precisely that 4-2x > 8 or 4-2x < -8.
 
Kk so i don't have to do the zeros. I redid the question.

-(4-2x)>8
-4+2X>8
2x>12
X>6

4-2x>8
-2x>4
x>-2

Interval notation

(-2,∞)
 
elmosworld403 said:
Kk so i don't have to do the zeros. I redid the question.

-(4-2x)>8
-4+2X>8
2x>12
X>6
OK
4-2x>8
-2x>4
x>-2
No, when you divide by sides by -2 you have to reverse the inequality, so the last line should be x < -2.
 
Are you sure that this should be in the calculus section?
 

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