Solve the equation for x: 2x+b=c

Question

Check this process:

Step 1: 2x+b−b=c−b

Step 2: 2x=c−b

Step 3: 2x−2=c−b−2

Step 4: x=c2−b−2

Check all of the choices that are true statements.

(2 points)
Responses

There is no error in the process.
There is no error in the process.

The process has an error from step 1 to step 2
The process has an error from step 1 to step 2

The process has an error from step 2 to step 3
The process has an error from step 2 to step 3

The process has an error from step 3 to step 4

Answer 1

Let's break down the given steps in solving the equation \(2x + b = c\):

1. Original Equation:
   \(2x + b = c\)

2. Step 1:
   \(2x + b - b = c - b\)
   This step is correct as it simplifies to \(2x = c - b\).

3. Step 2:
   \(2x = c - b\)
   This step is also correct.

4. Step 3:
   The given step states \(2x - 2 = c - b - 2\).
   This step is incorrect. It should rather have stayed as \(2x = c - b\).

5. Step 4:
   \(x = \frac{c - b - 2}{2}\) (if we were to try to get to this step from an incorrect step).
   However, since Step 3 contains an error, Step 4 can't be computed correctly based on erroneous information.

Conclusion:

• There is no error in the process until Step 2.
• The error occurs from Step 2 to Step 3.
• Consequently, Step 4 is also based on this incorrectness.

Valid Conclusions:

• There is no error in the process. (False)
• The process has an error from step 1 to step 2. (False)
• The process has an error from step 2 to step 3. (True)
• The process has an error from step 3 to step 4. (True)

Therefore, the true statements are:

• The process has an error from step 2 to step 3.
• The process has an error from step 3 to step 4.