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 has an error. The correct answer is x=−4b−c
The process has an error. The correct answer is x is equal to negative 4 b minus c

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=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 is correct.

Answer 1

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:

1. The process has an error. The correct answer is \( x = -4b - c \) - **Incorrect.**
2. The process has an error. The correct answer is \( x \) is equal to negative \( 4b - c \) - **Incorrect.**
3. The process has an error. The correct answer is \( x = 2c - \frac{2}{3}b \) - **Correct.**
4. The process has an error. The correct answer is \( x \) is equal to \( 2c - \frac{2}{3}b \) - **Correct.**
5. The process has an error. The correct answer is \( x = \frac{4bc}{3} \) - **Incorrect.**
6. 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.