If `(-(1)/(2)) xx (x - 5) + 3 = - (5)/(2)`, then what is the value of x ?

Options

A. 16
B. 4
C. -6
D. -4

Answer

To solve the equation \(-\frac{1}{2}(x - 5) + 3 = -\frac{5}{2}\), we will follow these steps:

### Step 1: Isolate the term with \(x\)
First, we want to isolate the term that contains \(x\). We can do this by moving the constant \(3\) to the right side of the equation.

\[ -\frac{1}{2}(x - 5) = -\frac{5}{2} - 3 \]

### Step 2: Simplify the right side
Next, we need to simplify the right side of the equation. We can convert \(3\) into a fraction with a denominator of \(2\):

\[ 3 = \frac{6}{2} \]

Now substituting this into the equation gives:

\[ -\frac{1}{2}(x - 5) = -\frac{5}{2} - \frac{6}{2} \]

Combining the fractions on the right side:

\[ -\frac{1}{2}(x - 5) = -\frac{11}{2} \]

### Step 3: Eliminate the negative fraction
To eliminate the negative fraction, we can multiply both sides of the equation by \(-2\):

\[ x - 5 = 11 \]

### Step 4: Solve for \(x\)
Now, we can solve for \(x\) by adding \(5\) to both sides:

\[ x = 11 + 5 \]

Thus,

\[ x = 16 \]

### Final Answer
The value of \(x\) is \(16\).

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