Question

9. Solve 3x+2b=6c
for x.

Step 1: 3x+2b−2b=6c−2b
subtract 2b from both sides

Step 2: 3x=6c−2b
combine like terms/simplify

Step 3: 3x3=6c3−2b
divide by 3 on both sides to get x isolated

Step 4: x=2c−2b
simplify/final answer

Which statement is TRUE?

(1 point)
Responses

The process is correct.
The process is correct.

The process has an error. The correct answer is x=4bc3
The process has an error. The correct answer is x is equal to the fraction with numerator 4 b c and denominator 3

The process has an error. The correct answer is x=2c−23b
The process has an error. The correct answer is x is equal to 2 c minus 2 thirds b

The process has an error. The correct answer is x=−4b−c

Answer 1

Let's carefully analyze the steps given to see if the isolation of \( x \) is performed correctly in the equation \( 3x + 2b = 6c \).

Starting with the original 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:
We have:
\[
3x = 6c - 2b
\]
**This step is also correct.**

### Step 3:
Divide both sides by \( 3 \) to get \( x \) isolated:
\[
x = \frac{6c - 2b}{3}
\]

To simplify:
\[
x = \frac{6c}{3} - \frac{2b}{3}
\]
This simplifies to:
\[
x = 2c - \frac{2}{3}b
\]
**This step is correct and gives us the final answer.**

### Final Answer:
So the final correct expression for \( x \) is:
\[
x = 2c - \frac{2}{3}b
\]

### Evaluating Options:
Now, looking at the provided options:
- The statement that "the process is correct" is true but does not represent the final answer.
- The statement “The process has an error. The correct answer is \( x=2c−2b \)” is false.
- The statement “The process has an error. The correct answer is \( x=−4b−c \)” is false.

The option that states: “The process has an error. The correct answer is \( x \) is equal to \( 2c−\frac{2}{3}b \)” or its equivalent wording could be true, but it's not explicitly listed in your options.

Since the final answer accurately reflects the steps showing \( x \) to be \( 2c - \frac{2}{3}b \), and given the context, **the conclusion is**:
- "The process is correct" in isolation, but the final answer representation needs to state \( \frac{2}{3}b \) to be entirely accurate.

### Conclusion:
The truthful statement should be that the process is correct, but it has an error in final presentation. The correct answer is:
\[
x = 2c - \frac{2}{3}b
\]