Solve the mathematical problem involving absolute value. 3 - I 2/3 x -6 I + 2
9
-3
1
-21
To solve this problem, we need to evaluate two absolute values separately and then add them together.
First, let's evaluate the absolute value of (2/3)x - 6:
| (2/3)x - 6 |
Next, let's evaluate the absolute value of -2:
| -2 |
Note that the absolute value of any negative number is equal to its positive counterpart.
Finally, let's add the two absolute values together:
| (2/3)x - 6 | + | -2 |
This problem cannot be solved without further information.
Just answer the dang question
Apologies for the confusion. Let's solve the mathematical problem involving absolute value.
3 - |2/3x - 6| + 2 = 9
We need to isolate the absolute value first. Subtracting 3 and 2 from both sides gives:
- |2/3x - 6| = 9 - 3 - 2,
- |2/3x - 6| = 4.
Now, we need to consider two cases for the absolute value:
Case 1: 2/3x - 6 ≥ 0 (no need to change the absolute value):
2/3x - 6 = 4.
Adding 6 to both sides:
2/3x = 10.
Multiplying both sides by 3/2:
x = 15.
Case 2: 2/3x - 6 < 0 (changing the sign of the absolute value):
-(2/3x - 6) = 4.
Expanding and removing the negative:
-2/3x + 6 = 4.
Subtracting 6 from both sides:
-2/3x = -2.
Multiplying both sides by -3/2:
x = 3.
So the solutions to the equation are x = 15 and x = 3.
These are the answers
9
-3
1
-21
Apologies for the confusion. Let's solve the mathematical problem involving absolute value.
3 - |2/3x - 6| + 2 = 9
First, let's evaluate the absolute value of (2/3)x - 6:
| (2/3)x - 6 |
Next, let's simplify the equation:
3 - |(2/3)x - 6| + 2 = 9
Combine like terms:
5 - |(2/3)x - 6| = 9
Now, let's consider two cases for the absolute value:
Case 1: (2/3)x - 6 ≥ 0
In this case, the absolute value can be removed without changing its sign:
5 - ((2/3)x - 6) = 9
5 - (2/3)x + 6 = 9
(2/3)x - 1 = 9
(2/3)x = 10
x = 15
Case 2: (2/3)x - 6 < 0
In this case, the absolute value needs to be written as -(2/3)x + 6:
5 - (-(2/3)x + 6) = 9
5 + (2/3)x - 6 = 9
(2/3)x - 1 = 9
(2/3)x = 10
x = 15
So the solution to the equation is x = 15.
That’s not one of the answers
Apologies for the confusion. Let's solve the mathematical problem involving absolute value.
3 - |2/3x - 6| + 2 = 9
First, let's evaluate the absolute value of (2/3x - 6):
|2/3x - 6|
Next, let's simplify the equation:
3 - |2/3x - 6| + 2 = 9
Combine like terms:
5 - |2/3x - 6| = 9
Now, let's consider two cases for the absolute value:
Case 1: 2/3x - 6 ≥ 0
In this case, the absolute value can be removed without changing its sign:
5 - (2/3x - 6) = 9
5 - 2/3x + 6 = 9
-2/3x + 11 = 9
-2/3x = -2
x = 3
Case 2: 2/3x - 6 < 0
In this case, the absolute value needs to be written as -(2/3x - 6):
5 - (-(2/3x - 6)) = 9
5 + 2/3x - 6 = 9
2/3x - 1 = 9
2/3x = 10
x = 15
The solutions to the equation are x = 3 and x = 15.