16. 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

Answer 1

Let's go through each step of the given process to identify any errors:

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

2. Step 1: Subtract \(b\) from both sides \[ 2x + b - b = c - b \] This simplifies to: \[ 2x = c - b \] (This step is correct.)

3. Step 2: Simplifying the equation: \[ 2x = c - b \] (This step is correct.)

4. Step 3: The step states: \[ 2x - 2 = c - b - 2 \] This is incorrect. From step 2, we should not subtract 2 from \(2x\) as there is no reason to do so. Therefore, there's an error here. The correct next step should have been to divide both sides by 2, leading to: \[ x = \frac{c - b}{2} \]

5. Step 4: Following from an incorrect Step 3: The statement \(x = c2 - b - 2\) also does not follow logically from the previous steps and is therefore incorrect.

Summary of True Statements:

• There is an error in the process from step 2 to step 3.
• Since step 3 contains an error, it affects the following step 4, which also contains an error.

Final Evaluation of Options:

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

Conclusion:

The correct responses are:

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