To solve the mathematical problem involving absolute value:
Step 1: Start by solving the expression inside the absolute value bars.
In this case, the expression is: 2/3x - 6
Step 2: Set up two separate equations, one with the expression inside the absolute value bars as positive, and one with it as negative.
Equation 1: 2/3x - 6 = 3
Equation 2: 2/3x - 6 = -3
Step 3: Solve both equations separately.
For Equation 1:
Add 6 to both sides:
2/3x = 9
Multiply both sides by 3/2 to isolate x:
x = 9 * 3/2
x = 27/2
For Equation 2:
Add 6 to both sides:
2/3x = 3
Multiply both sides by 3/2 to isolate x:
x = 3 * 3/2
x = 9/2
Step 4: Check the solutions in the original absolute value expression.
For x = 27/2:
3 - |2/3(27/2) - 6| + 2
Simplify the expression inside the absolute value bars:
3 - |9 - 6| + 2
Simplify the absolute value:
3 - |3| + 2
Evaluate the absolute value:
3 - 3 + 2 = 2
For x = 9/2:
3 - |2/3(9/2) - 6| + 2
Simplify the expression inside the absolute value bars:
3 - |3 - 6| + 2
Simplify the absolute value:
3 - |-3| + 2
Evaluate the absolute value:
3 - 3 + 2 = 2
Step 5: Both solutions x = 27/2 and x = 9/2 satisfy the original absolute value expression.
Solve the mathematical problem involving absolute value.
3 - I 2/3 x -6 I + 2
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