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

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

GPT-4o mini · Answer

Let's go through each step of the process you provided to check for errors:

Starting equation: \[ 2x + b = c \]
Step 1: \[ 2x + b - b = c - b \] This step is correct. We subtracted \( b \) from both sides, which simplifies to \( 2x = c - b \).
Step 2: \[ 2x = c - b \] This is also correct as per the previous step's outcome.
Step 3: \[ 2x - 2 = c - b - 2 \] This step introduces an error. The left side starts from \( 2x \), and there is no reason to subtract 2 at this point if we haven't done so on the right side. The proper step following Step 2 would be to solve for \( x \) by dividing both sides by 2: \[ x = \frac{c - b}{2] \]
Step 4: \[ x = \frac{c}{2} - b - 2 \] This step is also incorrect as it does not logically follow the previous steps and introduces incorrect terms.

Given this analysis:

The process has an error from step 2 to step 3 and from step 3 to step 4.
There was no error from step 1 to step 2.