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

Answer 1

Let's check each step of the equation for correctness:

1. Starting with the original equation:
\[
2x + b = c
\]

2. **Step 1: Subtract \(b\) from both sides**
\[
2x + b - b = c - b
\]
This simplifies correctly to:
\[
2x = c - b
\]
No error here.

3. **Step 2: Rewrite the equation**
\[
2x = c - b
\]
This is correct as stated. No error here.

4. **Step 3: The step states**
\[
2x - 2 = c - b - 2
\]
This step introduces an additional \(-2\) to both sides, which is not correct based on the previous line. The operation is not valid in terms of maintaining equality.

5. **Step 4: The process states**
\[
x = \frac{c^2 - b - 2}{2}
\]
Since Step 3 itself was incorrect, this equation can't be derived correctly from the previous ones.

So, to summarize:

- There is no error in Step 1.
- There is no error in Step 2.
- There **is an error from Step 2 to Step 3**.
- There **is an error from Step 3 to Step 4**.

Correct options based on the evaluation:

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

Thus, the true statements would be those concerning the errors in steps 3 and 4.