# Find x14*|3x-2|=28

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to move all terms to one side, such that:

`14*|3x-2| - 28 = 0`

You need to factor out `14` , such that:

`14*(|3x-2| - 2) = 0`

Since `14!=0,` hence `|3x-2| - 2 = 0 => |3x-2| = 2.`

Using absolute value definition, yields:

`3x - 2 = +-2 => {(3x - 2 = 2, x >= 2/3),(3x - 2 = -2, x < 2/3):}`

`{(3x = 4, x >= 2/3),(3x = 0, x < 2/3):} => {(x = 4/3, x >= 2/3),(x = 0, x < 2/3):}`

Hence, evaluating the solutions to absolute value equation yields ` x = 0, x = 4/3.`

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll apply the property of absolute value:

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 belongs to 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 belongs to the interval of admissible values, (-infinite, 2/3), we'll accept it.