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)ResponsesThere is no error in the process.There is no error in the process.The process has an error from step 1 to step 2The process has an error from step 1 to step 2The process has an error from step 2 to step 3The process has an error from step 2 to step 3The process has an error from step 3 to step 4

Answer 1

Let's check each step in the process to see if there are any errors.

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

2. Step 1: \(2x + b - b = c - b\) This simplifies to \(2x = c - b\), which is correct.

3. Step 2: \(2x = c - b\) No error here; it is correct.

4. Step 3: \(2x - 2 = c - b - 2\) This suggests that 2 was subtracted from both sides. However, to isolate \(x\), we should divide \(2x\) by 2 instead. This step should have been isolating \(x\) as follows: \[ \frac{2x}{2} = \frac{c - b}{2}. \] So, there is an error here.

5. Step 4: \(x = \frac{c - b - 2}{2}\) This step is incorrect based on the previous error in Step 3. The correct expression is: \[ x = \frac{c - b}{2}. \]

Now, let's summarize the findings:

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

True statements:

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

So the responses "There is no error in the process" and "The process has an error from step 1 to step 2" are false.

In conclusion, the correct choices are:

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