How to solve second grade inequality with modulo? The result is -3 and 3, and I get the result 3 and -1

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Answer 1 · 2018-05-10T16:38:45

#color(blue)(x=+-3)#

For absolute value equations we have to solve both:

#x-2=3/x# and #-x-2=3/(-x)#

#x-2=3/x#

#x^2-2x-3=0#

Factor:

#(x+1)(x-3)=0=>x=-1 and x=3#

#-x-2=3/(-x)#

#x^2+2x-3=0#

Factor:

#(x+3)(x-1)=0=>x=-3 and x=1#

We now check with original equation:

For #x=1#

#|1|-2=3/(|1|)#

#-1!=3#

For #x=-3#

#|-3|-2=3/(|-3|)#

#1=1# True

For #x=-1#

#|-1|-2=3/(|-1|)#

#-1!=3#

For #x=3#

#|3|-2=3/(|3|)#

#1=1# True

So, solutions are:

#x=+-3#