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**

We have to solve |3x+6|=9

As the absolute value of (3x + 6) is equal to 9, the actual value of 3x + 6 can be 9 or -9.

This gives 3x + 6 = 9

=> x = 3/3 = 1

and 3x + 6 = -9

=> 3x = -15

=> x = -5

**The required values of x are x = 1 and x = -5.**

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}.**