. 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 evaluate each step in the process to determine if there are any errors.

1. Step 1: \( 2x + b - b = c - b \)
   This simplifies to \( 2x = c - b \).
   (Correct)

2. Step 2: \( 2x = c - b \)
   This is the correct simplification from step 1.
   (Correct)

3. Step 3: \( 2x - 2 = c - b - 2 \)
   This step is incorrect because it subtracts 2 from both sides without a corresponding operation on the left side. The correct step should be to divide both sides by 2 if we are solving for \( x \).
   (Error)

4. Step 4: \( x = \frac{c - b - 2}{2} \)
   This is also incorrect as it comes from a false step 3; further, the formula to isolate \( x \) should be \( x = \frac{c - b}{2} \).
   (Error)

Now let’s summarize our findings:

• 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

So 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.