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