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# sum of roots of equation ||x - 1| - 5|= 6 is?

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sum of roots of equation ||x - 1| - 5|= 6 is?

#1
+85958
+15

We have that either,

l x -1 l - 5  = 6           or  that   (l x -1 l - 5)  = - 6

Working with the first, we have

l x - 1 l   = 11     which implies that

x - 1 = 11          and       x - 1  = -11

So  x = 12          and  x = -10

And working with the second, we have

l x - 1 l - 5  = -6

l x - 1 l = -1      which is impossible

So,  the sum of the roots = 2

CPhill  Feb 8, 2015
Sort:

#1
+85958
+15

We have that either,

l x -1 l - 5  = 6           or  that   (l x -1 l - 5)  = - 6

Working with the first, we have

l x - 1 l   = 11     which implies that

x - 1 = 11          and       x - 1  = -11

So  x = 12          and  x = -10

And working with the second, we have

l x - 1 l - 5  = -6

l x - 1 l = -1      which is impossible

So,  the sum of the roots = 2

CPhill  Feb 8, 2015

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