Let's review the steps provided to solve the equation \( 3x + 2b = 6c \) for \( x \).
Step 1:
Starting with the equation:
\[ 3x + 2b = 6c \]
Subtract \( 2b \) from both sides:
\[ 3x + 2b - 2b = 6c - 2b \]
This simplifies to:
\[ 3x = 6c - 2b \]
Step 2:
This step is already reflected as:
\[ 3x = 6c - 2b \]
The equation is simplified.
Step 3:
Now, divide both sides by 3 to isolate \( x \):
\[ \frac{3x}{3} = \frac{6c - 2b}{3} \]
This simplifies to:
\[ x = 2c - \frac{2b}{3} \]
Step 4:
Here, the statement in the original process suggests:
\[ x = 2c - 2b \]
However, upon comparing this with the actual simplification, we found that:
\[ x = 2c - \frac{2b}{3} \]
Thus, the conclusion \( x = 2c - 2b \) in the original statements is incorrect.
Now, let's evaluate the options:
- A. x = -4b - c (Incorrect)
- B. x = 4bc/3 (Incorrect)
- C. x = 2c - 2/3b (Correct based on our derivation)
- D. The process is correct (Incorrect)
Thus, the correct answer is: C. The process has an error. The correct answer is x = 2c - 2/3b.