If `8-[7-{x-(4-7/2)}] = 5`, then the value of `x` is:

Options

A. 5
B. 4.5
C. 3.2
D. 2.5

Answer

To solve the equation \( 8 - [7 - \{ x - (4 - \frac{7}{2}) \}] = 5 \), we will follow these steps:

### Step 1: Simplify the expression inside the brackets
Start by simplifying the innermost expression:
\[ 4 - \frac{7}{2} \]
Convert \( 4 \) to a fraction with a denominator of \( 2 \):
\[ 4 = \frac{8}{2} \]
Now, substitute this back into the expression:
\[ 4 - \frac{7}{2} = \frac{8}{2} - \frac{7}{2} = \frac{1}{2} \]

### Step 2: Substitute back into the equation
Now substitute \( \frac{1}{2} \) back into the equation:
\[ 8 - [7 - (x - \frac{1}{2})] = 5 \]

### Step 3: Simplify the brackets
Now simplify the expression inside the brackets:
\[ 7 - (x - \frac{1}{2}) = 7 - x + \frac{1}{2} = 7 + \frac{1}{2} - x = \frac{14}{2} + \frac{1}{2} - x = \frac{15}{2} - x \]
So the equation now becomes:
\[ 8 - \left(\frac{15}{2} - x\right) = 5 \]

### Step 4: Distribute the negative sign
Distributing the negative sign gives:
\[ 8 - \frac{15}{2} + x = 5 \]

### Step 5: Combine like terms
Convert \( 8 \) to a fraction with a denominator of \( 2 \):
\[ 8 = \frac{16}{2} \]
Now substitute:
\[ \frac{16}{2} - \frac{15}{2} + x = 5 \]
This simplifies to:
\[ \frac{1}{2} + x = 5 \]

### Step 6: Isolate \( x \)
To isolate \( x \), subtract \( \frac{1}{2} \) from both sides:
\[ x = 5 - \frac{1}{2} \]
Convert \( 5 \) to a fraction:
\[ 5 = \frac{10}{2} \]
So:
\[ x = \frac{10}{2} - \frac{1}{2} = \frac{9}{2} \]

### Step 7: Final answer
Thus, the value of \( x \) is:
\[ \boxed{4.5} \]

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