How do you solve the inequality #abs(3x-4)<20#?

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Answer 1 · 2016-01-19T07:23:33

#x in(-16/3,8)#

Removing the abs the equation became:

#-20<3x-4<20#

This is equivalent to the follow system:

#:.{ ((3x-4)> -20), ((3x -4)<20) :}#

#{ (3x> -20+4), (3x <20+4) :}#

#{ (3x> -16), (3x <24) :}#

#{ (x> -16/3), (x <8) :}#

Drawing the inequality system graph we have to pick up the #x# interval where both the lines are continuos:

enter image source here

#:.x in(-16/3,8)#

Answer 2 · 2016-01-26T21:00:44

(-16/3, 8)

#|3x-4|<20# is equivalent to

#3x-4<20 and -(3x-4)<20#

In the second expression if we multiply both parcels by -1, we must invert the signal:

#3x-4<20 and 3x-4> -20#

Now, we add 4 in both sides of the inequality:

#3x<24 and 3x> -16#

Then we divide by 3

#x<8 and x> -16/3#

so the solution is the interval

(-16/3, 8)