How do you solve #abs(x-2)<5x#?

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Answer 1 · 2018-07-21T11:59:39

The solution is #x in (1/3,+oo)#

The inequality with absolute value is

#|x-2|<5x#

#x-2=0#

#=>#, #x=2#

There are #2# intervals to consider

#I_1=(-oo,2)# and #I_2=(2,+oo)#

Therefore,

In the first interval #I_1#

#-x+2<5x#

#6x>2#

#x>1/3#

This solution #in I_1#

In the first interval #I_2#

#x-2<5x#

#4x>2#

#x>1/2#

This solution #!in I_2#

The only solution is #x in (1/3,+oo)#

graph{|x-2|-5x [-5.55, 5.55, -2.773, 2.776]}