Let's evaluate each step of the process given for solving the equation \(2x + b = c\):
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Step 1: \(2x + b - b = c - b\)
- This step is correct. When you subtract \(b\) from both sides, you maintain the equality.
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Step 2: \(2x = c - b\)
- This step is also correct. The equation simplifies to \(2x = c - b\) after \(b\) is cancelled out.
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Step 3: \(2x - 2 = c - b - 2\)
- This step contains an error. The correct move from \(2x = c - b\) should be to isolate \(x\); there is no justification for subtracting 2 from both sides here.
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Step 4: \(x = \frac{c}{2} - b - 2\)
- Since the previous step was incorrect, this equation is also incorrect. The correct logic from \(2x = c - b\) is to divide both sides by 2 to get \(x = \frac{c - b}{2}\).
Now that we have analyzed each step, let's evaluate the choices:
- A. There is no error in the process: False (there is an error).
- B. The process has an error from step 1 to step 2: False (steps 1 and 2 are correct).
- C. The process has an error from step 2 to step 3: True (this is where the first error occurs).
- D. The process has an error from step 3 to step 4: True (because step 3 was incorrect, step 4 is also incorrect).
Thus, the true statements are: C and D.