11. Solve the mathematical problem involving absolute value. 3 - I 2/3 x -6 I + 2 * 2 points 9 -3 1 -21
To solve the mathematical problem involving absolute value, we follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
First, we simplify the expression inside the absolute value:
2/3 x -6 = (-12/3) + (2/3)x = -4 + (2/3)x
Now, let's work with each part individually:
The expression 3 - I 2/3 x -6 I can be rewritten as:
3 - |(-4 + (2/3)x)|
We consider the case where (-4 + (2/3)x) is negative:
(-4 + (2/3)x) < 0
We remove the absolute value signs and reverse the inequality sign:
3 - (-4 + (2/3)x) = 3 + 4 - (2/3)x = 7 - (2/3)x
Next, we consider the case where (-4 + (2/3)x) is positive:
(-4 + (2/3)x) > 0
We can leave the expression as is without changing anything: -4 + (2/3)x
Now, we put both cases together:
3 - I 2/3 x -6 I + 2 =
-4 + (2/3)x + 2 if (-4 + (2/3)x) > 0
7 - (2/3)x if (-4 + (2/3)x) < 0
Therefore, the solution cannot be determined without knowing the value of x.