11. Solve the mathematical problem involving absolute value. %0D%0A3 - I 2/3 x -6 I + 2 %0D%0A*%0D%0A2 points%0D%0A9%0D%0A-3%0D%0A1%0D%0A-21
To solve the mathematical problem involving absolute value, let's break it down into steps:
Step 1: Simplify the expression inside the absolute value signs.
3 - I2/3x - 6I + 2
Step 2: Remove the absolute value signs and consider both cases: positive and negative.
Case 1: 3 - I2/3x - 6I + 2
Case 2: -(3 - I2/3x - 6I + 2)
Step 3: Solve each case separately.
Case 1: 3 - I2/3x - 6I + 2
Combine like terms:
5 - I2/3x - 6I
Case 2: -(3 - I2/3x - 6I + 2)
Distribute the negative sign:
-3 + I2/3x + 6I - 2
Step 4: Set up the equations for each case.
Case 1: 5 - I2/3x - 6I = 9
Case 2: -3 + I2/3x + 6I - 2 = 9
Step 5: Solve each equation.
Case 1:
Combine like terms:
- I2/3x - 6I = 4
Case 2:
Combine like terms:
I2/3x + 6I = 14
Step 6: Simplify and solve for x in each case.
Case 1:
Multiply both sides by -1 to eliminate the negative sign:
I2/3x + 6I = -4
Case 2:
Divide both sides by 2/3 to isolate x:
2/3x + 9I = 7
Subtract 9I from both sides:
2/3x = 7 - 9I
Multiply both sides by 3/2:
x = (7 - 9I) * 3/2
Simplify:
x = 21/2 - 27/2I
Step 7: Write the solutions for each case.
Case 1: x = 21/2 - 27/2I
Case 2: x = 21/2 - 27/2I
Therefore, the solutions to the mathematical problem involving absolute value are:
x = 21/2 - 27/2I, - (21/2 - 27/2I)
so what's the absolute value
The absolute value of a number, denoted by |x|, is the distance between that number and zero on the number line. In other words, it is the positive value of the number without considering its sign.
For example:
|3| = 3, because the distance from 3 to 0 is 3.
|-5| = 5, because the distance from -5 to 0 is 5.
In general, if x is a real number, the absolute value of x is defined as follows:
- If x is greater than or equal to 0, then |x| = x.
- If x is less than 0, then |x| = -x.
The absolute value function is used to ensure that the result is always positive or zero.
Can you pick one of then answer above that is close to being correct
Apologies for any confusion. Let's correctly solve the problem involving absolute value using the information provided:
Given: 3 - |2/3x - 6| + 2
To solve this, we need to consider the two cases when the expression inside the absolute value is positive or negative.
Case 1: 2/3x - 6 ≥ 0
This means that 2/3x - 6 is greater than or equal to zero. Solving for x:
2/3x - 6 ≥ 0
2/3x ≥ 6
x ≥ (6 * 3) / 2
x ≥ 9
In this case, the absolute value will be positive, so we keep the expression as it is.
So, the first part of the equation becomes:
3 - (2/3x - 6) + 2
Simplifying further:
3 - 2/3x + 6 + 2
= 11 - 2/3x
Case 2: 2/3x - 6 < 0
This means that 2/3x - 6 is less than zero. Solving for x:
2/3x - 6 < 0
2/3x < 6
x < (6 * 3) / 2
x < 9
In this case, the absolute value changes the sign of the expression inside it, so we have:
3 - (-(2/3x - 6)) + 2
Simplifying further:
3 + 2/3x - 6 + 2
= -1 + 2/3x
Putting together the cases:
When 2/3x - 6 ≥ 0:
3 - |2/3x - 6| + 2 = 11 - 2/3x
When 2/3x - 6 < 0:
3 - |2/3x - 6| + 2 = -1 + 2/3x
So, depending on the value of x, the equation simplifies to either 11 - 2/3x or -1 + 2/3x.
11. Solve the mathematical problem involving absolute value. 3- |2/3 multiply -6| +2.
a. 9
b. -3
c. 1
d. -21
To solve the mathematical problem involving absolute value, let's follow these steps:
Step 1: Simplify the expression inside the absolute value by performing the multiplication:
|2/3 * -6| becomes | -4 |
Step 2: Calculate the absolute value:
|-4| = 4
Step 3: Substitute the absolute value back into the original expression:
3 - 4 + 2
Step 4: Perform the subtraction and addition:
(-4 + 3) + 2 = -1 + 2 = 1
Therefore, the solution to the mathematical problem is:
3 - |2/3 * -6| + 2 = 1
Hence, the correct option is c. 1.