An equation and the steps to solve it are shown below:
3x − one over two (8x − 2) = 4
Step 1: 3x − 4x + 1 = 4
Step 2: x + 1 = 4
Step 3: x + 1 − 1 = 4 − 1
Step 4: x = 3
Which step was the error made and why?
Step 1, because incorrect signs have been used
Step 2, because the terms have been added incorrectly
Step 3, because numbers have been added to both sides of the equation
No error was made
pls help me
does 3x - 4x = x?
In this case, the error was made in Step 3. Let's go through the steps and identify the mistake:
Step 1: 3x − one over two (8x − 2) = 4
In this step, we distribute the "one over two" factor to the expression (8x - 2):
3x - (1/2)(8x) - (1/2)(-2) = 4
This simplifies to:
3x - 4x + 1 = 4
Step 2: x + 1 = 4
Here, we combine like terms by subtracting 4x from 3x, which gives us x, and leave the +1 term as it is.
Step 3: x + 1 − 1 = 4 − 1
In this step, the error occurs. We have subtracted 1 from both sides of the equation, but instead, we should have subtracted 1 from only the right side of the equation:
x + 1 - 1 = 3
Step 4: x = 3
Since the error occurred in Step 3, the value of x we end up with is incorrect. Therefore, the error was made in Step 3 - "because numbers have been added to both sides of the equation."
To correct the mistake, we should only subtract 1 from the right side of the equation:
x + 1 = 3 - 1
x + 1 = 2
Therefore, the correct equation and steps to solve it would be:
3x − one over two (8x − 2) = 4
Step 1: 3x - (1/2)(8x) - (1/2)(-2) = 4
Step 2: 3x - 4x + 1 = 4
Step 3: -x + 1 = 4
Step 4: -x = 4 - 1
Step 5: -x = 3
Step 6: x = -3 (after multiplying both sides by -1)
Hope this clarification helps! Let me know if you have any further questions.