How do you solve #|4- \frac{2}{3} x | > 8#?

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Answer 1 · 2018-04-18T18:10:44

#(-oo,-6)U(18, oo)#

#|4 - 2/3 x| > 8#

This is solved by analyzing if the number is + or -
Then

#a) 4 - 2/3 x > 8#

#-2/3 x > 8 - 4#

#-2/3 x > 4#

#- x > ((4)(3))/2#

#- x(-1) > 6(-1)#

#x < -6#

#(-oo,-6)#

#b) - 4 + 2/3 x > 8#

#2/3 x > 8 + 4#

#2/3 x > 12#

#x > ((12)(3))/(2)#

#x > 18#

#(18, oo)#

Then

#(-oo,-6)U(18, oo)#