Solve the mathematical problem involving absolute value. 3 - I 2/3 x -6 I + 2

Question

9
-3
1
-21

Answer 1

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.

Answer 2

Just answer the dang question

Answer 3

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.

Answer 4

These are the answers
9
-3
1
-21

Answer 5

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.

Answer 6

That’s not one of the answers

Answer 7

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.