How do you solve # |x| - |x-7| = 7#?

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Answer 1 · 2016-04-15T21:01:50

#x>=7#

You have to divide the resolution into three parts:

1)if x<=0: the equation turns into:

#-x-(-x+7)=7#

#-x+x-7=7#

#0=14#

No solution

2) if #0 < x<=7# : the equation turns into:

#x-(-x+7)=7#

#x+x-7=7#

#2x=14#

#x=7# (solution)

3)if # x>=7#: the equation turns into:

#x-(x-7)=7#

#x-x+7=7#

#0=0# Universal solution (all values are possible, but remember we limited this part to x>=7)

Joining all the solution of the three branches we obtain solution as #x>=7#.