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 \((-1/2) \cdot (x - 5) + 3 = -5/2\), we will follow these steps:

### Step 1: Distribute the \(-1/2\)
We start by distributing \(-1/2\) to both terms inside the parentheses:

\[ (-1/2) \cdot (x - 5) = (-1/2) \cdot x + (-1/2) \cdot (-5) = -\frac{x}{2} + \frac{5}{2} \]

Now, substituting this back into the equation gives us:

\[ -\frac{x}{2} + \frac{5}{2} + 3 = -\frac{5}{2} \]

### Step 2: Combine the constants
Next, we need to combine the constants on the left side. We can convert \(3\) into a fraction with a denominator of \(2\):

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

So now the equation looks like this:

\[ -\frac{x}{2} + \frac{5}{2} + \frac{6}{2} = -\frac{5}{2} \]

Adding \(\frac{5}{2}\) and \(\frac{6}{2}\):

\[ -\frac{x}{2} + \frac{11}{2} = -\frac{5}{2} \]

### Step 3: Isolate the term with \(x\)
Now, we will isolate the term with \(x\) by subtracting \(\frac{11}{2}\) from both sides:

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

Combining the right side:

\[ -\frac{x}{2} = -\frac{16}{2} \]

### Step 4: Solve for \(x\)
Now we can solve for \(x\) by multiplying both sides by \(-2\):

\[ x = 16 \]

### Final Answer
Thus, the value of \(x\) is:

\[ \boxed{16} \]

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