Find x . Determine x if |3x+6|=9 .

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It is given that |3x+6|=9

As the absolute value of 3x + 6 is equal to 9 either 3x + 6 = 9 or -(3x + 6) = 9

3x + 6 = 9

=> 3x = 3

=> x = 1

-(3x + 6) = 9

=> 3x + 6 = -9

=> 3x = -15

=> x = -5

The solutions of x are x = 1 and x = -5

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What you have to do is solve for two possible equations.  They are

3x + 6 = 9

and

-(3x + 6) = 9 which is the same as

-3x - 6 = 9

So you must solve both:

3x + 6 = 9

3x = 3

x = 1

-3x - 6 = 9

-3x = 15

x = -5

So the answer for this is x = -5,1

Approved by eNotes Editorial Team