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=c/2−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
The process has an error from step 3 to step 4

Answer 1

Let’s analyze each step of the process to identify any errors.

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

   • This step is correct because subtracting \(b\) from both sides is a valid operation.

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

   • This step is correct as well. After removing \(b\) from both sides, you correctly simplified the equation.

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

   • This step is incorrect. Instead of subtracting \(2\) from both sides, the equation should remain \(2x = c - b\). There was no mention of the number \(2\) in the original equation that would necessitate subtracting \(2\).

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

   • Because Step 3 is incorrect, Step 4 is also incorrect. From the correctly simplified Step 2 (\(2x = c - b\)), the proper next step should be dividing both sides by 2 to get \(x = \frac{c - b}{2}\).

Based on this analysis, we can conclude:

• There is an error from step 2 to step 3.
• The later steps are also incorrect due to the mistake in step 3.

The true statements from the response options would be:

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

The false statements include:

• There is no error in the process.
• The process has an error from step 1 to step 2.

So, you should select the statements indicating errors between step 2 and step 3, and between step 3 and step 4.