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Which of the following
represents this inequality?
|3x – 4| < 6x

Which of the following represents this inequality? |3x – 4| < 6x-example-1
User Immutable
by
8.8k points

1 Answer

11 votes

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

User Vikram Sapate
by
8.0k points

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