Determine the number of solutionsDetermine the number of solutions of the equation |4x-4| -12=0? ( one or two? )

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use absolute value definition, such that:

`|4x - 4| = {(4x - 4, 4x - 4>=0),(4 - 4x, 4x - 4 < 0):}`

`|4x - 4| = {(4x - 4, x >= 1),(4 - 4x, x < 1):}`

Considering `x in [1,oo)` yields:

`4x - 4 - 12 = 0 => 4x = 16 => x = 4 in [1,oo)`

Considering `x in(-oo,1)` yields:

`4 - 4x - 12 = 0 => -4x - 8 = 0 => -4x = 8 => x = -2 in (-oo,1)`

Hence, evaluating the solutions to the given absolute value equation, yields `x = 4, x = -2` .

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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By definition, the absolute value means:

|p| = a>0

We'll have to solve 2 cases:

1) 4x-4 = 12

We'll add 4 both sides:

4x = 12 + 4

4x = 16

We'll divide by 4:

x = 4

2) 4x-4 = -12

We'll add 4 both sides, to isolate x to the left side:

4x = -12 + 4

4x = -8

We'll divide by 4:

x = -2

The equation has 2 solutions : {-2 ; 4}.

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