16. 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 the steps in the process of solving the equation for \( x \): \( 2x + b = c \).

Step-by-step Analysis:

1. Step 1: \( 2x + b - b = c - b \)

   • This step is correct. You are isolating \( 2x \) by subtracting \( b \) from both sides.

2. Step 2: \( 2x = c - b \)

   • This step is also correct. It simplifies the equation from Step 1.

3. Step 3: \( 2x - 2 = c - b - 2 \)

   • This step contains an error. Instead of subtracting \( 2 \), you should be dividing both sides by \( 2 \) to isolate \( x \).

4. Step 4: \( x = \frac{c - b - 2}{2} \)

   • This step would be incorrect as the previous step was already incorrect.

Conclusion:

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

Responses to check:

• False: There is no error in the process.
• True: 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.