Let's review the given steps for solving the equation \( 3x + 2b = 6c \) for \( x \):
Starting equation:
\[ 3x + 2b = 6c \]
Step 1:
Subtract \( 2b \) from both sides:
\[ 3x + 2b - 2b = 6c - 2b \]
This simplifies to:
\[ 3x = 6c - 2b \]
(This step is correct.)
Step 2:
This step just restates what we found in Step 1:
\[ 3x = 6c - 2b \]
(This step is also correct.)
Step 3:
Divide both sides by 3:
\[ \frac{3x}{3} = \frac{6c - 2b}{3} \]
This simplifies to:
\[ x = \frac{6c - 2b}{3} \]
Or, you can separate the terms in the numerator:
\[ x = \frac{6c}{3} - \frac{2b}{3} \]
This further simplifies to:
\[ x = 2c - \frac{2}{3}b \]
(This step shows a misunderstanding in the original answer provided.)
Step 4:
The final answer presented in the original process was:
\[ x = 2c - 2b \]
That is incorrect.
Now comparing it to the provided options:
- The process has an error. The correct answer is \( x = \frac{4bc}{3} \) (This is incorrect.)
- The process has an error. The correct answer is \( x \) is equal to the fraction with numerator \( 4bc \) and denominator \( 3 \) (This is incorrect.)
- The process has an error. The correct answer is \( x = 2c - \frac{2}{3}b \) (This is correct.)
- The process has an error. The correct answer is \( x \) is equal to \( 2c - \frac{2}{3}b \) (This is also correct.)
- The process has an error. The correct answer is \( x = -4b - c \) (This is incorrect.)
- The process is correct. (This is incorrect.)
Thus, the correct statement regarding the given process is:
The process has an error. The correct answer is \( x = 2c - \frac{2}{3}b \).