Question

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

Answer 1

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

Explanation:

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)`

Answer 2

(-16/3, 8)

Explanation:

`|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)