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

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

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

Nov 29, 2015

#1
+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   Nov 29, 2015
edited by CPhill  Nov 29, 2015
edited by CPhill  Nov 30, 2015

#1
+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   CPhill Nov 29, 2015
edited by CPhill  Nov 29, 2015
edited by CPhill  Nov 30, 2015