Solve and show your work:  3x - 2 = |x + 6|

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation 3x - 2 = |x + 6| has to be solved.

The absolute value of a number, |x| = x for `x >=0` and it is equal to -x for x < 0.

3x - 2 = |x + 6| gives two equations

3x - 2 = x + 6 and 3x - 2 = -x - 6

=> 2x = 8 and 4x = -4

=> x = 4 and x = -1

The solution of 3x - 2 = |x + 6| is x = 4 and x = -1

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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First we need to define ` |x + 6|` .

`|x + 6|>= 0` always.

Then;

If `x>=-6` then ` |x + 6| = (x+6)`

If `x< -6` then `|x + 6|= -(x+6)`

 

`When x>=-6`

`3x-2 = |x + 6|`

`3x-2 = x+6`

    ` 2x = 8 `

      `x = 4`

 

 

`When x<-6`

`3x-2 = |x + 6|`

`3x-2 = -(x+6)`

    ` 4x = -4`

      `x = -1`

 

So the answers are;

x = 4 when `x>=-6`

x = -1 when `x<-6`

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