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 = c/2 - b - 2
check all of the choices that are true statements
A. there is no error in the process
B. the process has an error from step 1 to step 3
C. the process has an error from step 2 to step 3
D. the process has an error from step 3 to step 4
The correct answer is D. The error occurs in step 3, where the equation is simplified incorrectly. The correct simplification should be:
2x - 2 + c - b = c - b - 2
So, the correct solution is x = (c - b - 2)/2
are you sure that is the only answer
You are correct, I apologize for the confusion in my previous response. Actually, multiple answers could be correct for this problem. Here is the correct explanation:
In step 3, the equation simplifies to:
2x - 2 + c - b = c - b - 2
From here, we can see that the terms "-2" and "-b" on both sides of the equation cancel out:
2x - 2 + c - b = c - b - 2
Simplifying further:
2x + c - b = c - b
Now, we can subtract "c" from both sides to isolate the "x" on the left side:
2x + c - b - c = c - b - c
Simplifying:
2x - b = -b
Dividing both sides by 2:
(2x - b)/2 = -b/2
This gives us two possible solutions:
x - (b/2) = -b/2
or
x = -b/2
So, the correct answer is:
E. The process has an error in step 3, but there are multiple correct solutions depending on the value of "b."
The correct answer is D.
There is an error in step 3 to step 4:
Instead of subtracting 2 from both sides of the equation, it should be subtracting 'b' from both sides. The correct step is:
2x - 2 = c - b
The correct answer is:
x = (c - b)/2
To solve the equation 2x + b = c, we need to isolate the variable x. Now, let's go through each step of the given process to check if there are any errors:
Step 1: 2x + b - b = c - b
In this step, we are subtracting b from both sides of the equation to eliminate it from the left side. This step is correct.
Step 2: 2x = c - b
Here, we successfully eliminated b from the left side of the equation. This step is also correct.
Step 3: 2x - 2 + c - b - 2
In this step, we seem to be subtracting 2 from both sides of the equation. However, since this step is not clearly explained, it is difficult to determine its accuracy. It is possible that this is a mistake.
Step 4: x = c/2 - b - 2
In this final step, we are dividing both sides of the equation by 2 to isolate the variable x. We also correctly subtract b and 2 from the right side. This step appears to be correct.
Based on the given process, we can conclude that there is a potential error from Step 3 to Step 4. Thus, the correct answer is:
D. the process has an error from step 3 to step 4.