Find x .Determine x if |3x+6|=9 .

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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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pohnpei397 | College Teacher | (Level 3) Distinguished Educator

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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

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jess1999 | Student, Grade 9 | (Level 1) Valedictorian

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 | 3x + 6 | = 9

To solve this use the equations 

3x + 6 = 9        and.    3x + 6 = -9     now subtract 6 on both side of both equation

By subtracting, you should get

3x = 3         and         3x = -15 now divide both sides of both equation by 3

By dividing, you should get

x = 1       and  x = -5 which are your answers

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We recall that the absolute value means:

|p| = a>0

We'll have to solve 2 cases:

1) 3x+6 = 9

We'll subtract 6 both sides:

3x = 9 - 6

3x = 3

We'll divide by 3:

x = 1

2) 3x+6 = -9

We'll subtract 6 both sides, to isolate x to the left side:

3x = -6 - 9

3x = -15

We'll divide by 3:

x = -5

The equation has 2 solutions : {-5 ; 1}.

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