Question

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

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
The process has an error from step 3 to step 4
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Answer 1

Let's analyze each step of the process to identify any errors:

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

2. **Step 1: Rearranging the equation**
The equation is manipulated by subtracting \( b \) from both sides:
\( 2x + b - b = c - b \)
This simplifies correctly to:
\( 2x = c - b \)
**(Correct)**

3. **Step 2: Result from Step 1**
From Step 1, we have:
\( 2x = c - b \)
This is carried forward correctly into Step 2.
**(Correct)**

4. **Step 3: Solving for \( x \)**
The equation \( 2x = c - b \) can be manipulated to isolate \( x \).
The erroneous operation in Step 3 suggests:
\( 2x - 2 = c - b - 2 \)
This is incorrect. Instead, to solve for \( x \), you would divide both sides by 2:
\( x = \frac{c - b}{2} \)
**(Error in Step 3)**

5. **Step 4: Incorrect manipulation**
Step 4 stated:
\( x = c2 - b - 2 \)
This is incorrect since it doesn't follow from the previous correct manipulations.
**(Error in Step 4)**

### Conclusion:
- There is an error from **Step 2 to Step 3** where incorrect subtraction and manipulation occur.
- There is also an error in **Step 3 to Step 4** due to incorrect computation.

### True Statements:
- **The process has an error from step 2 to step 3.**
- **The process has an error from step 3 to step 4.**

The other options are incorrect. The process does contain errors.