# how many solutions has equation |4x-4|=12? ( one or two? )

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| 4x - 4 | = 12

Since there's an absolute value sign, change this equation to

**4x - 4 = -12 and 4x -4 =12 **now add 4 on both sides on both equation

By adding, you should get

**4x = -8 and 4x = 16 **now divide by 4 on both sides and on both equation

By dividing, your equation should look like

**x = -2 and x = 4**

So your answer is **x = -2 ; 4 **

**So there are two solutions **

To find the number of solutions : |4x-4| = 12.

When 4x-4 >= 0, |4x-4| = 12 implies 4x- 4. = 12.

4x-4+4 = 12+4 = 16.

4x = 16

4x/4 = 16/4 = 4.

x = 4.

When 4x-4 < = 0, | 4x-4| = 12 implies 4x-12 = -12.

4x-4 +4 = -12 +4 = -8

4x = -8.

Therefore 4x/4 = -8/2 = -2.

x= -2.

Thus there are two solution for x: x= 4 and x = -2.

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}.**