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Can someone tell me how to solve this double absolute inequality?

 

||3-x|-2x|<=9

Guest Nov 29, 2015

Best Answer 

 #1
avatar+78557 
+10

||3-x|-2x|<=9

 

Remember that if   a = m, then    l a l   =  m,  if a> 0   or  l a l  =  -m,  if a < 0

 

Taking 3-x out of the absolute value bars, we have that either

 

l 3 - x - 2x l < = 9          or  that          l -3  + x - 2x l <  =  9

 

And likewise, we have that

 

3 - x - 2x < = 9             or that            3 - x + 2x < = 9

 

                                   simplify

 

3 - 3x < =  9                                        x + 3 < = 9

 

-3x < = 6                                             x < =  6

 

x >= -2       

 

So      -2 <= x <=  6

 

 

 

cool cool cool                                                                                 

CPhill  Nov 29, 2015
edited by CPhill  Nov 29, 2015
edited by CPhill  Nov 30, 2015
Sort: 

1+0 Answers

 #1
avatar+78557 
+10
Best Answer

||3-x|-2x|<=9

 

Remember that if   a = m, then    l a l   =  m,  if a> 0   or  l a l  =  -m,  if a < 0

 

Taking 3-x out of the absolute value bars, we have that either

 

l 3 - x - 2x l < = 9          or  that          l -3  + x - 2x l <  =  9

 

And likewise, we have that

 

3 - x - 2x < = 9             or that            3 - x + 2x < = 9

 

                                   simplify

 

3 - 3x < =  9                                        x + 3 < = 9

 

-3x < = 6                                             x < =  6

 

x >= -2       

 

So      -2 <= x <=  6

 

 

 

cool cool cool                                                                                 

CPhill  Nov 29, 2015
edited by CPhill  Nov 29, 2015
edited by CPhill  Nov 30, 2015

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