Determine x if |3x+6|=9.

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x =1 ?

To solve this, you need to split your first equation into two equations. This is because |3x+6| can equal 3x + 6 or it can equal -(3x+6) which is -3x - 6.

So you need to solve two equations: 3x + 6 = 9 and -3x - 6 = 9.

Now it's simple:

3x + 6 = 9

3x = 3

x = 1

-3x - 6 = 9

-3x = 15

x = -5

**So the answer is that x = -5,1**

Because of the absolute value definition, we'll have to discuss two cases:

1) 3x + 6 , for 3x + 6 > 0

x>-6/3 => x>-2

3x + 6 = 9

3x = 9 - 6

3x = 3

x = 1

Since 1 is bigger than -2, we'll accept it as solution.

2) -3x - 6, for 3x + 6 < 0

3x < -6

x < -2

3x + 6 = -9

3x = -15

x = -5

Since -5 < -2, then we'll accept it as solution.

**The equation will have 2 possible solutions: {-5 ; 1}.**

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