How do you solve #-8<=2x-4<6#?

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Answer 1 · 2018-03-02T11:55:10

Using both inequalities. See below

From #-8<=2x-4# Sum 4 to both sides

#4-8<=2x-4+4#

#-4<=2x# and then #-2<=x# this is the same that #x>=-2#

Now, From #2x-4<6# Add 4 to both sides

#2x-4+4<6+4# and then

#2x<10# Which is #x<5#

Collecting all results, we have #x# must be #x>=-2# and #x<5#

This is the interval #[-2, 5)# The solution is all #x# belonging to this interval #x in [-2,5)# or using set notation

#{x in RR// x>=-2 and x<5}#

Answer 2 · 2018-03-02T12:01:04

Solution : #-2<= x <5 # In interval notation: #x| [ -2 , 5)#

# -8 <= 2x-4 <6 or -8+4 <= 2x-4+4 <6+4# or

#-4<= 2x <10 or -4/2<= (2x)/2 <10/2 # or

#-2<= x <5 :. # Solution : #-2<= x <5 #

In interval notation: #x| [ -2 , 5)# [Ans]