Given `w = -2, x = 3, y = 0` & `z = -(1)/(2)`. Find the value of 2x(w-z).
A. -9
B. 9
C. 8
D. -8

Options

A. B
B. D
C. A
D. C

Answer

To solve the problem, we need to find the value of the expression \( 2x(w - z) \) given the values \( w = -2 \), \( x = 3 \), \( y = 0 \), and \( z = -\frac{1}{2} \).

### Step 1: Substitute the values into the expression
We start with the expression:
\[ 2x(w - z) \]
Substituting the values of \( x \), \( w \), and \( z \):
\[ 2 \cdot 3 \cdot (-2 - (-\frac{1}{2})) \]

### Step 2: Simplify the expression inside the parentheses
Now, simplify \( w - z \):
\[ w - z = -2 - (-\frac{1}{2}) = -2 + \frac{1}{2} \]
To combine these, we can convert \(-2\) into a fraction:
\[ -2 = -\frac{4}{2} \]
Now we can add:
\[ -\frac{4}{2} + \frac{1}{2} = -\frac{4 - 1}{2} = -\frac{3}{2} \]

### Step 3: Substitute back into the expression
Now we substitute back into the expression:
\[ 2 \cdot 3 \cdot (-\frac{3}{2}) \]

### Step 4: Calculate the multiplication
First, calculate \( 2 \cdot 3 \):
\[ 2 \cdot 3 = 6 \]
Now multiply by \(-\frac{3}{2}\):
\[ 6 \cdot (-\frac{3}{2}) = -\frac{18}{2} = -9 \]

### Final Answer
Thus, the value of \( 2x(w - z) \) is:
\[ \boxed{-9} \]