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

The process is correct.
The process is correct.

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

Answer 1

Let's go through the steps provided to solve the equation \( 3x + 2b = 6c \) for \( x \):

1. **Start with the equation:**
\( 3x + 2b = 6c \)

2. **Step 1:** Subtract \( 2b \) from both sides:
\( 3x + 2b - 2b = 6c - 2b \)
This simplifies to:
\( 3x = 6c - 2b \)

3. **Step 2:** This is already done in Step 1, so we have:
\( 3x = 6c - 2b \)

4. **Step 3:** Divide both sides by \( 3 \):
\( \frac{3x}{3} = \frac{6c - 2b}{3} \)
This simplifies to:
\( x = \frac{6c - 2b}{3} \)

5. **Step 4:** Further simplify:
\( x = \frac{6c}{3} - \frac{2b}{3} \)
This simplifies to:
\( x = 2c - \frac{2b}{3} \)

The correct final answer is:
\[ x = 2c - \frac{2b}{3} \]

Now, comparing this with the provided statements:
- The statement "The process has an error. The correct answer is x=2c−23b" is correct.

Thus, the correct response is:
**The process has an error. The correct answer is x is equal to \( 2c - \frac{2b}{3} \).**