Find the value of v :
`10 (1)/(2) - [8(1)/(2) + { 7 - bar(6-4)}] bar(6-4)`=2 (v)

Options

A. -3
B. -2
C. 1
D. 4

Answer

To solve the equation step by step, we will follow the order of operations as per BODMAS/BIDMAS rules, which stands for Brackets, Orders (i.e., powers and roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

Given equation:
\[ 10 \frac{1}{2} - \left[ 8 \frac{1}{2} + \{ 7 - \bar{(6-4)} \} \right] \bar{(6-4)} = 2v \]

### Step 1: Simplify the bar notation
The bar notation indicates that we should calculate the value inside the bar first. Here, we have:
\[ \bar{(6-4)} = 2 \]
So we can replace \(\bar{(6-4)}\) with \(2\).

### Step 2: Substitute the value
Now, substitute \(2\) into the equation:
\[ 10 \frac{1}{2} - \left[ 8 \frac{1}{2} + \{ 7 - 2 \} \right] \cdot 2 = 2v \]

### Step 3: Calculate the expression inside the brackets
First, calculate \(7 - 2\):
\[ 7 - 2 = 5 \]
Now substitute this back into the equation:
\[ 10 \frac{1}{2} - \left[ 8 \frac{1}{2} + 5 \right] \cdot 2 = 2v \]

### Step 4: Calculate the mixed numbers
Convert the mixed numbers to improper fractions:
\[ 10 \frac{1}{2} = \frac{21}{2} \]
\[ 8 \frac{1}{2} = \frac{17}{2} \]

### Step 5: Substitute the improper fractions
Now substitute these values back into the equation:
\[ \frac{21}{2} - \left[ \frac{17}{2} + 5 \right] \cdot 2 = 2v \]

### Step 6: Calculate the expression inside the brackets
Convert \(5\) to a fraction:
\[ 5 = \frac{10}{2} \]
Now substitute:
\[ \frac{21}{2} - \left[ \frac{17}{2} + \frac{10}{2} \right] \cdot 2 = 2v \]

### Step 7: Combine the fractions
Combine the fractions inside the brackets:
\[ \frac{17}{2} + \frac{10}{2} = \frac{27}{2} \]
Now substitute this back:
\[ \frac{21}{2} - \left[ \frac{27}{2} \right] \cdot 2 = 2v \]

### Step 8: Multiply by 2
Now multiply \(\frac{27}{2}\) by \(2\):
\[ \frac{27}{2} \cdot 2 = 27 \]
So the equation becomes:
\[ \frac{21}{2} - 27 = 2v \]

### Step 9: Convert \(27\) to a fraction
Convert \(27\) to a fraction:
\[ 27 = \frac{54}{2} \]
Now substitute:
\[ \frac{21}{2} - \frac{54}{2} = 2v \]

### Step 10: Subtract the fractions
Now perform the subtraction:
\[ \frac{21 - 54}{2} = 2v \]
\[ \frac{-33}{2} = 2v \]

### Step 11: Divide by 2
Now divide both sides by \(2\):
\[ v = \frac{-33}{4} \]

### Final Answer
Thus, the value of \(v\) is:
\[ v = -\frac{33}{4} \]