How do you solve the inequality #| 3x - 4 | > | 2x + 1 |#?

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Answer 1 · 2016-06-03T13:31:55

#color(red)((-oo, 3/5] uu [5, +oo))#

Given #abs(3x-4)>abs(2x+1)#

#+(3x-4)>2x+1#

#+(3x-4+4-2x)>2x+1+4-2x#

#color(red)(x>5)#

#-(3x-4)>2x+1#

#-3x+4>2x+1#

#-3x-2x+4-4>2x-2x+1-4#

#-5x#>#-3#

Dividing by #-5# will change #># to #<#

#(-5x)/(-5)#<#(-3)/(-5)#

#color(red)(x)##color(red)(<)##color(red)(3/5)#

God bless....I hope the explanation is useful.