Let's evaluate the steps provided to solve the equation \( 3x + 2b = 6c \) for \( x \).
Step 1:
Starting with the original equation:
\[ 3x + 2b = 6c \]
Subtract \( 2b \) from both sides:
\[ 3x + 2b - 2b = 6c - 2b \]
This simplifies to:
\[ 3x = 6c - 2b \]
This step is correct.
Step 2:
This step combines like terms, and since there are no like terms to combine further:
\[ 3x = 6c - 2b \]
This step is also correct.
Step 3:
To isolate \( x \), divide both sides by \( 3 \):
\[ x = \frac{6c - 2b}{3} \]
This simplifies to:
\[ x = 2c - \frac{2b}{3} \]
So this step is correct in terms of isolating \( x \).
Step 4:
In the final answer:
Different from what was stated, the correct simplified expression should be:
\[ x = 2c - \frac{2}{3}b \]
This means that the final answer \( x = 2c - 2b \) is not correct.
Now, to analyze the provided response statements:
- The process has an error. The correct answer is \( x = -4b - c \) - Incorrect.
- The process has an error. The correct answer is \( x \) is equal to negative \( 4b - c \) - Incorrect.
- The process has an error. The correct answer is \( x = 2c - \frac{2}{3}b \) - Correct.
- The process has an error. The correct answer is \( x \) is equal to \( 2c - \frac{2}{3}b \) - Correct.
- The process has an error. The correct answer is \( x = \frac{4bc}{3} \) - Incorrect.
- The process is correct - Incorrect.
Therefore, the true statements are:
- The process has an error. The correct answer is \( x = 2c - \frac{2}{3}b \).
- The process has an error. The correct answer is \( x \) is equal to \( 2c - \frac{2}{3}b \).
If forced to select just one, you could choose either option 3 or 4, as they both communicate similar information.