How do you solve #3x-5 <2x-5 <5x-2#?

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Answer 1 · 2017-02-26T20:14:21

#-1 < x < 0#

Given: #" "3x-5<2x-5<5x-2" "# Inequality(1)

Lets get rid of one of the #x# terms

Subtract #2x# from every part

#x-5<-5<3x-2#

Add #5# to very part

#x<0<3x+3 " Inequality(2)"#
~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(brown)("Observation(1): So "x" is negative and "3x+3>0)#

Investigate #3x+3>0#

Factor out the 3

#3(x+1)>0#

Divide both sides by 3. Note that #0/3=0#

#x+1>0#

#x > -1" "#Inequality(3)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(brown)("Observation(2): Combining Inequality(3) with Inequality(2)")#

#-1 < x < 0#