Let's go through the steps outlined to solve the equation \(3x + 2b = 6c\) for \(x\) and verify the calculations:
Step 1: Start from the original equation:
\[
3x + 2b = 6c
\]
Subtract \(2b\) from both sides:
\[
3x = 6c - 2b
\]
(This is correct.)
Step 2: The equation now is:
\[
3x = 6c - 2b
\]
This is already simplified, so we can move to the next step.
Step 3: Divide both sides by 3 to isolate \(x\):
\[
x = \frac{6c - 2b}{3}
\]
This can be further simplified as:
\[
x = 2c - \frac{2b}{3}
\]
or alternatively, you can factor it:
\[
x = 2c - \frac{2}{3}b
\]
Step 4: The above analysis shows that the correct form of \(x\) is:
\[
x = \frac{6c - 2b}{3}
\]
or simplifying:
\[
x = 2c - \frac{2}{3}b
\]
Now, let's review what was provided in the above steps:
- The final answer given in the question was \(x = 2c - 2b\), which is incorrect.
The statements include a simplification error as \(2c - 2b\) ends up not being equivalent to the correct derivation.
Given these points:
- The correct simplified form is \(x = 2c - \frac{2}{3}b\).
- The statement provided that \(x = 2c - 2b\) is incorrect.
Thus, the true statement considering the entire process is that the final form given in the question about \(x\) is not accurate.
Final Answer: The statement in the steps that claims \(x = 2c - 2b\) is incorrect. The correct solution should be \(x = 2c - \frac{2}{3}b\).
