Compare the methodsWhat is the difference between solving |4x-4| =12 and 4x-4 =12?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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The difference between solving |4x-4| =12 and 4x-4 =12 is that in the first case |4x - 4| = 12 means (4x - 4) = 12 and 4x - 4 = -12

=> 4x = 16 and 4x = -8

=> x = 4 and x = -2

In the second case 4x - 4 = 12, we only get x = 4

The use of the absolute sign can give two separate expressions the same magnitude.

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First, we'll have to recall the definition of absolute value:

|p| = a>0

So, to solve |4x-4| =12 we'll have to consider 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 |4x-4| =12 has 2 solutions : {-2 ; 4}

While for the equation |4x-4| =12 we'll have to consider 2 solutions, for the linear equation 4x-4 =12 we'll have just a single solution, namely x = 4.

So, the difference stays in the number of possible values for x.

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