Solve the mathematical problem involving absolute value. 3 - I 2/3 x -6 I + 2
9 -3 1 -21
To solve the problem, we need to evaluate the absolute value expression and then solve for x.
First, we evaluate the absolute value expression:
|2/3x - 6| = 2
To simplify, we can break it into two separate equations:
2/3x - 6 = 2 or 2/3x - 6 = -2
Solving the first equation:
2/3x = 2 + 6
2/3x = 8
x = (8 * 3) / 2
x = 12
Solving the second equation:
2/3x = -2 + 6
2/3x = 4
x = (4 * 3) / 2
x = 6
Therefore, the solution to the problem is x = 12 or x = 6.
That’s not any of the answers
Apologies for the incorrect response. Let's reevaluate the problem.
The given equation is:
3 - |2/3x - 6| + 2
To solve this equation involving absolute value, we need to consider two cases:
Case 1: 2/3x - 6 is positive or zero.
In this case, the absolute value expression becomes 2/3x - 6, and the equation becomes:
3 - (2/3x - 6) + 2 = 9 - 3 + 1 - 21
Simplifying, we have:
2/3x - 1 = -12
Adding 1 to both sides:
2/3x = -11
Multiplying both sides by 3/2:
x = -33/2
Case 2: 2/3x - 6 is negative.
In this case, the absolute value expression becomes -(2/3x - 6), which simplifies to -2/3x + 6. The equation becomes:
3 - (-2/3x + 6) + 2 = 9 - 3 + 1 - 21
Simplifying, we have:
2/3x + 7 = -12
Subtracting 7 from both sides:
2/3x = -19
Multiplying both sides by 3/2:
x = -57/2
Therefore, the solutions to the equation are x = -33/2 and x = -57/2.
These are the answers
9
-3
1
-21
Apologies for the previous incorrect response. Let's solve the problem again.
The given equation is: 3 - |2/3x - 6| + 2
To solve this equation involving absolute value, we need to consider two cases:
Case 1: 2/3x - 6 is positive or zero.
In this case, the absolute value expression becomes 2/3x - 6, and the equation becomes:
3 - (2/3x - 6) + 2 = 9 - 3 + 1 - 21
Simplifying, we have:
-2/3x + 11 = -12
Adding 2/3x and 12 to both sides:
11 = 2/3x - 12
Adding 12 to both sides:
x = 33
Case 2: 2/3x - 6 is negative.
In this case, the absolute value expression becomes -(2/3x - 6), which simplifies to -2/3x + 6. The equation becomes:
3 - (-2/3x + 6) + 2 = 9 - 3 + 1 - 21
Simplifying, we have:
-2/3x + 1 = -12
Adding 2/3x and 12 to both sides:
1 = 2/3x - 12
Adding 12 to both sides:
x = 33/2
Therefore, the solutions to the equation are x = 33 and x = 33/2.
Not any of the answers
Apologies for the confusion. Let's solve the problem again with a different approach.
The given equation is: 3 - |2/3x - 6| + 2
To solve this equation involving absolute value, we need to consider two cases:
Case 1: 2/3x - 6 is positive or zero.
In this case, the absolute value expression becomes 2/3x - 6, and the equation becomes:
3 - (2/3x - 6) + 2 = 9 - 3 + 1 - 21
Simplifying, we have:
5/3x - 1 = -12
Adding 1 to both sides:
5/3x = -11
Multiplying both sides by 3/5:
x = -33/5
Case 2: 2/3x - 6 is negative.
In this case, the absolute value expression becomes -(2/3x - 6), which simplifies to -2/3x + 6. The equation becomes:
3 - (-2/3x + 6) + 2 = 9 - 3 + 1 - 21
Simplifying, we have:
-2/3x + 6 + 5 = -12
-2/3x + 11 = -12
Adding 2/3x and 12 to both sides:
11 = 2/3x - 12
Adding 12 to both sides:
x = 33/3
Therefore, the solutions to the equation are x = -33/5 and x = 33/3, which can be simplified to x = -6.6 and x = 11.