Find the value of x.
`6(3x + 2) - 5(6x - 1) = 6 (x - 3) - 5(7x - 6) + 12x`

Options

A. 2
B. `-1`
C. 1
D. 0

Answer

To solve the equation \( 6(3x + 2) - 5(6x - 1) = 6(x - 3) - 5(7x - 6) + 12x \), we will follow these steps:

### Step 1: Expand both sides of the equation
- Left side:
\[ 6(3x + 2) - 5(6x - 1) = 18x + 12 - 30x + 5 = -12x + 17 \]
- Right side:
\[ 6(x - 3) - 5(7x - 6) + 12x = 6x - 18 - 35x + 30 + 12x = -17x + 12 \]

### Step 2: Set the expanded equations equal to each other
Now we have:
\[ -12x + 17 = -17x + 12 \]

### Step 3: Rearrange the equation to isolate \( x \)
Add \( 17x \) to both sides:
\[ -12x + 17 + 17x = 12 \]
This simplifies to:
\[ 5x + 17 = 12 \]

### Step 4: Subtract 17 from both sides
\[ 5x = 12 - 17 \]
This simplifies to:
\[ 5x = -5 \]

### Step 5: Divide both sides by 5 to solve for \( x \)
\[ x = \frac{-5}{5} = -1 \]

### Final Answer
Thus, the value of \( x \) is \( -1 \).

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