What is x if 14*| 3x - 2 | = 28

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll solve the equation, expressing first the modulus.

Case 1:

l 3x-2 l = 3x - 2 for 3x-2 >= 0

3x >= 2

x >= 2/3

Now, we'll solve the equation:

14(3x-2) = 28

We'll divide by 14:

3x-2 = 2

3x = 4

x = 4/3

Since x = 4/3 is in the interval of admissible values,[2/3, +infinite], we'll accept it.

Case 2:

l 3x-2 l = -3x + 2 for 3x-2 < 0

3x<2

x<2/3

Now, we'll solve the equation:

14(-3x+2) = 28

-3x+2 = 2

 -3x = 0

x = 0

Since x = 0 is in the interval of admissible values, (-infinite, 2/3), we'll accept it.

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve for x in 14|3x-2| = 28.

We divide both sides by 14 first and the resulting equation is:

|3x-2| = 28/14 = 2.

|3x-2| = 2.

|3x-2| is 3x-2 , when 3x-2 > 0  or when x > 2/3.

So when x > 2/3 , 3x-2 = 2

3x = 2+2 = 4.

x = 4/3.

When x< 2/3,

|3x-2) = -(3x-2) = 2.

 2 -3x = 2.

2-2 = 3x.

 0  = 3x.

So x= 0.

Therefore x = 0 or x = 4/3 are the solutions.

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