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.
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 2 to step 3.
The process has an error from step 3 to step 4.
The correct process should be:
Step 1: 2x + b - b = c - b
Step 2: 2x = c - b
Step 3: (2x)/2 = (c - b)/2
Step 4: x = (c - b)/2
Checking all of the choices that are true statements:
Assuming b, c, and x are real numbers, the equation is linear, and the process is valid.
The correct answer is: The process has an error from step 1 to step 2.
In step 1, subtracting b from both sides of the equation would result in 2x = c - b, not c - b - 2. Therefore, step 3 and step 4 are also incorrect as they are based on the error in step 1.
The correct answer is: The process has an error from step 2 to step 3.
Explanation: Let's go through the steps one by one to identify the error.
Step 1: 2x + b - b = c - b (subtracting b from both sides)
Simplifying both sides: 2x = c - b
Step 2: 2x - 2 = c - b - 2 (subtracting 2 from both sides)
Here is where the mistake occurs. The correct operation should be dividing both sides by 2, not subtracting 2. Dividing by 2 enables us to isolate x.
The correct step should be:
2x/2 = (c - b)/2
Simplifying: x = (c - b)/2
So, the error is from step 2 to step 3.