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 examine each step of the process to solve for \( x \) in the equation \( 2x + b = c \):

Step 1: \( 2x + b - b = c - b \)
This step is correct. It correctly subtracts \( b \) from both sides.

Step 2: \( 2x = c - b \)
This step is also correct. It simplifies the equation by eliminating \( b \) from the left side.

Step 3: \( 2x - 2 = c - b - 2 \)
This step is incorrect. The left side \( 2x \) should have been simplified to find \( x \), and no subtraction of \( 2 \) should have happened here. Therefore, \( 2x - 2 \) does not logically follow from \( 2x = c - b \).

Step 4: \( x = \frac{c - b - 2}{2} \)
This step does not even follow from Step 3 due to the error in the previous step, and it's also incorrectly written.

Based on this breakdown, the true statements are:

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

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.

You can check your answers against these findings.