If `(6-18x) - (x-7)= 8,` then the value of x is ____

Options

A. `-5//19`
B. `-2//13`
C. `2//13`
D. `5//19`

Answer

To solve the equation \( (6 - 18x) - (x - 7) = 8 \), we will follow these steps:

### Step 1: Simplify the left-hand side
Start by distributing the negative sign in the expression:
\[ (6 - 18x) - (x - 7) = 6 - 18x - x + 7 \]

### Step 2: Combine like terms
Combine the constant terms and the \(x\) terms:
\[ 6 + 7 - 18x - x = 13 - 19x \]
So, the equation now looks like:
\[ 13 - 19x = 8 \]

### Step 3: Isolate the variable term
To isolate the term with \(x\), subtract 13 from both sides:
\[ -19x = 8 - 13 \]
This simplifies to:
\[ -19x = -5 \]

### Step 4: Solve for \(x\)
Now, divide both sides by -19 to solve for \(x\):
\[ x = \frac{-5}{-19} \]
This simplifies to:
\[ x = \frac{5}{19} \]

### Final Answer
Thus, the value of \(x\) is:
\[ \boxed{\frac{5}{19}} \]