How do you solve #abs(x-2)>x+4#?

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Answer 1 · 2018-07-02T14:24:46

The solution is #x in (-oo,-1)#

This is solving an inequality with absolute values.

#x-2=0#, #=>#, #x=2#

There are #2# intervals to consider

#(-oo, 2)# and #(2,+oo)#

In the Interval #(-oo,2)#

#-x+2>x+4#

#=>#, #2x<-2#

#=>#, #x<-1#

As # x<-1# #in# the interval, the solution is accepted

In the Interval #(2,+oo)#

#x-2>x+4#

#=>#, #0>6#

There is no solution in the interval.

The solution is #x in (-oo,-1)#

graph{|x-2|-x-4 [-18.01, 18.02, -9, 9.01]}