Question

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.