Answer:
x>
4
9
Explanation:
|3x−4|<6x
Let's find the critical points of the inequality.
|3x−4|=6x
We know either3x−4=6xor3x−4=−6x
3x−4=6x(Possibility 1)
3x−4−6x=6x−6x(Subtract 6x from both sides)
−3x−4=0
−3x−4+4=0+4(Add 4 to both sides)
−3x=4
−3x
−3
=
4
−3
(Divide both sides by -3)
x=
−4
3
3x−4=−6x(Possibility 2)
3x−4+6x=−6x+6x(Add 6x to both sides)
9x−4=0
9x−4+4=0+4(Add 4 to both sides)
9x=4
9x
9
=
4
9
(Divide both sides by 9)
x=
4
9
Check possible critical points.
x=
−4
3
(Doesn't work in original equation)
x=
4
9
(Works in original equation)
Critical points:
x=
4
9
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x<
4
9
(Doesn't work in original inequality)
x>
4
9
(Works in original inequality)
Answer:
x>
4
9