Finding x Determine x if |3x+6|=9.
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,554 answers
starTop subjects are Math, Science, and Business
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.
calendarEducator since 2009
write35,413 answers
starTop subjects are History, Literature, and Social Sciences
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}.
x =1 ?
Student Answers