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

Answer 1

Hazel Anglin

#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:

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

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Answer 2

Abigail Allen

(-16/3, 8)

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

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

If we multiply both parcels by -1 in the second expression, we have to invert the signal:

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

We now add 4 to the inequality on both sides:

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

Next, we divide by three.

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

thus the interval provides the solution.

(-16/3, 8)

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Answer 3

Kennedy Adams

To solve the inequality (|3x - 4| < 20), you first isolate the absolute value expression and then split it into two separate inequalities: (3x - 4 < 20) and (- (3x - 4) < 20). Then solve each inequality separately to find the solution set for (x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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

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