If `(x)/(12) + (1)/(2) = x - 5,` then `x = "___."`

Options

A. 2
B. 4
C. 8
D. 6

Answer

To solve the equation \(\frac{x}{12} + \frac{1}{2} = x - 5\), we will follow these steps:

### Step 1: Eliminate the fractions
To eliminate the fractions, we can multiply every term in the equation by the least common multiple (LCM) of the denominators. The denominators are 12 and 2, and their LCM is 12.

\[ 12 \left(\frac{x}{12}\right) + 12 \left(\frac{1}{2}\right) = 12(x - 5) \]

### Step 2: Simplify each term
Now, we simplify each term:

\[ x + 6 = 12x - 60 \]

### Step 3: Rearrange the equation
Next, we will rearrange the equation to get all terms involving \(x\) on one side and constant terms on the other side.

Subtract \(x\) from both sides:

\[ 6 = 12x - x - 60 \]

This simplifies to:

\[ 6 = 11x - 60 \]

### Step 4: Isolate \(x\)
Now, add 60 to both sides to isolate the term with \(x\):

\[ 6 + 60 = 11x \]

This simplifies to:

\[ 66 = 11x \]

### Step 5: Solve for \(x\)
Finally, divide both sides by 11 to solve for \(x\):

\[ x = \frac{66}{11} \]

This simplifies to:

\[ x = 6 \]

### Final Answer
Thus, the value of \(x\) is \(6\).

---