If `8.8-{5(1)/(2)-(7(1)/(2)+2.8+x)}xx4.25+(0.2)^(2)=306` the value of x is

Options

A. `1.75`
B. `3.5`
C. 7
D. `1.4`

Answer

To solve the equation \( 8.8 - \left( 5 \frac{1}{2} - \left( 7 \frac{1}{2} + 2.8 + x \right) \right) \times 4.25 + (0.2)^2 = 306 \), we will follow the steps below:

### Step 1: Convert Mixed Numbers to Decimals
First, convert the mixed numbers to decimals:
- \( 5 \frac{1}{2} = 5 + 0.5 = 5.5 \)
- \( 7 \frac{1}{2} = 7 + 0.5 = 7.5 \)

### Step 2: Substitute the Values
Substituting these values into the equation gives:
\[ 8.8 - \left( 5.5 - \left( 7.5 + 2.8 + x \right) \right) \times 4.25 + (0.2)^2 = 306 \]

### Step 3: Simplify Inside the Brackets
Now simplify the expression inside the brackets:
\[ 7.5 + 2.8 = 10.3 \]
Thus, we have:
\[ 8.8 - \left( 5.5 - (10.3 + x) \right) \times 4.25 + (0.2)^2 = 306 \]

### Step 4: Further Simplify
Now, simplify \( 5.5 - (10.3 + x) \):
\[ 5.5 - 10.3 - x = -4.8 - x \]
So the equation becomes:
\[ 8.8 - (-4.8 - x) \times 4.25 + (0.2)^2 = 306 \]

### Step 5: Expand the Equation
Now we expand the equation:
\[ 8.8 + (4.8 + x) \times 4.25 + 0.04 = 306 \]
Calculating \( (4.8 + x) \times 4.25 \):
\[ 4.8 \times 4.25 = 20.4 \]
So we have:
\[ 8.8 + 20.4 + 4.25x + 0.04 = 306 \]

### Step 6: Combine Like Terms
Combine the constant terms:
\[ 8.8 + 20.4 + 0.04 = 29.24 \]
Thus, the equation simplifies to:
\[ 29.24 + 4.25x = 306 \]

### Step 7: Isolate the Variable
Now, isolate \( 4.25x \):
\[ 4.25x = 306 - 29.24 \]
Calculating the right side:
\[ 306 - 29.24 = 276.76 \]
So we have:
\[ 4.25x = 276.76 \]

### Step 8: Solve for \( x \)
Now, divide both sides by 4.25:
\[ x = \frac{276.76}{4.25} \]
Calculating the division:
\[ x = 65.12 \]

### Final Answer
The value of \( x \) is \( 65.12 \).

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