Question

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: 3x/3 = 6c/3 - 2b divide by 3 on both sides to get x isolated
Step 4: x = 2c - 2b simplify/final answer
Which statement is TRUE?
A. The process has an error. The correct answer is x = -4b - c
B. The process has an error. The correct answer is x = 4bc/3
C. The process has an error. The correct answer is x = 2c - 2/3b
D. The process is correct.

Answer 1

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

**Step 1:**
Starting with the equation:
\[ 3x + 2b = 6c \]
Subtract \( 2b \) from both sides:
\[ 3x + 2b - 2b = 6c - 2b \]
This simplifies to:
\[ 3x = 6c - 2b \]

**Step 2:**
This step is already reflected as:
\[ 3x = 6c - 2b \]
The equation is simplified.

**Step 3:**
Now, divide both sides by 3 to isolate \( x \):
\[ \frac{3x}{3} = \frac{6c - 2b}{3} \]
This simplifies to:
\[ x = 2c - \frac{2b}{3} \]

**Step 4:**
Here, the statement in the original process suggests:
\[ x = 2c - 2b \]
However, upon comparing this with the actual simplification, we found that:
\[ x = 2c - \frac{2b}{3} \]
Thus, the conclusion \( x = 2c - 2b \) in the original statements is incorrect.

Now, let's evaluate the options:
- A. x = -4b - c (Incorrect)
- B. x = 4bc/3 (Incorrect)
- C. x = 2c - 2/3b (Correct based on our derivation)
- D. The process is correct (Incorrect)

Thus, the correct answer is:
**C. The process has an error. The correct answer is x = 2c - 2/3b.**