9. Solve 3x+2b=6c

Question

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 \( 2c - \frac{2b}{3} \).