SOLUTION: I don't know how to solve this inequalitie.: It gave me this information. y=x^2 , squareroot y= squareroot x^2, squareroot y=|x| where therefore since x The question is |x-3|>|2x+

Question 125946: I don't know how to solve this inequalitie.: It gave me this information. y=x^2 , squareroot y= squareroot x^2, squareroot y=|x|
where therefore since x The question is |x-3|>|2x+1|
I asked this question before but is there another way to figure this out without graphing like can we actually solve it by doing the math?
Answer by stanbon(48551) (Show Source):
You can put this solution on YOUR website!
|x-3|>|2x+1|
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if x = 0, you get |-3|>|1|, which is true: so x=0 is part of the solution.
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If both x-3 and 2x+1 are positive you get:
x-3 > 2x+1
x<-4
Testing x=-10 you get:
|-13| > |-19| which is false.
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If both x-3 and 2x+1 are negative you get:
-x+3 > -2x-1
x > -4
Testing x=0 you know already this is true so x>-4 is part of the solution.
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If x-3 is positive and 2x+1 is negative you get:
x-3 > -2x-1
3x > 2
x>2/3
Testing x=1 you get:
|1-3| > |2+1| which is false
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If x-3 is negative and 2x+1 is positive you get:
-x+3 > 2x+1
3x<2
x <2/3
Testing 0 you know already this is true so x < 2/3
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Putting that all together you get -4 < x < 2/3
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PS: Graphing it is easier.
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Cheers,
Stan H.