Question
When solving the problem 45x-3
45x-3
=
4x+6
5x 3 = x+6
4x
X =
-
=
9
94
Was this correct?
(1 point)
=
16+6, your friend does the following:
Yes, this is correct. No error was made.
No, the bases of 4 and 16 should have both been changed to a base of 2.
No, in step 1 when the 16 changed to 4, it should have been 4² and the 2 distributed to
the current exponent.
No, in step 2, the 4 should have been distributed to the current exponents. This would
change the equation and yield a different final answer.
45x-3
=
4x+6
5x 3 = x+6
4x
X =
-
=
9
94
Was this correct?
(1 point)
=
16+6, your friend does the following:
Yes, this is correct. No error was made.
No, the bases of 4 and 16 should have both been changed to a base of 2.
No, in step 1 when the 16 changed to 4, it should have been 4² and the 2 distributed to
the current exponent.
No, in step 2, the 4 should have been distributed to the current exponents. This would
change the equation and yield a different final answer.
Answers
GPT-4o mini
To properly evaluate whether your friend's steps were correct or not, we need to review where potential mistakes could have been made, particularly if they changed bases or exponents incorrectly.
The original equation seems to contain a number of calculations that aren't clear due to formatting issues. However, here’s a step-by-step breakdown to clarify the statements regarding bases and exponents that your friend claimed:
1. **Change of base**: If an equation involves powers of different bases, it is often clearer to convert both sides of an equation to the same base for simplification. If your friend changed bases from 4 to 16, it definitely should have been correctly justified, especially if those bases relate to exponents being added or subtracted.
2. **Handling exponents**:
- If 16 was changed to \(4^2\), this means that the exponent should have been distributed to any other terms in the equation according to the rules of exponents (i.e., \( (a^m)^n = a^{m \cdot n} \)).
- It's crucial to keep track of exponents when one side of an equation is manipulated compared to the other.
3. **Distribution of exponents**:
- If during simplification or manipulation, the exponents on one side were not properly distributed through the equation, this could lead to an incorrect result.
Considering your friend made specific claims about the correctness of each step, we can break down the answer options:
- "Yes, this is correct. No error was made." — This can only be true if all the manipulation and steps were correct, which needs verification.
- "No, the bases of 4 and 16 should have both been changed to a base of 2." — This is a valid assertion, as it is often easier to work in a common base.
- "No, in step 1 when the 16 changed to 4, it should have been \(4^2\) and the 2 distributed to the current exponent." — If the exponent was not handled correctly, then this would indeed be a crucial error.
- "No, in step 2, the 4 should have been distributed to the current exponents. This would change the equation and yield a different final answer." — Failing to distribute correctly can certainly lead to different outcomes.
Conclusively, without the exact expressions and logical steps provided, it’s difficult to definitively state which of your friend’s arguments holds true in your specific calculation. However, care must always be taken when manipulating exponents and changing bases in any equations.
If you would like to share the specific problem you were trying to solve, I'd be happy to give you a clearer answer!
The original equation seems to contain a number of calculations that aren't clear due to formatting issues. However, here’s a step-by-step breakdown to clarify the statements regarding bases and exponents that your friend claimed:
1. **Change of base**: If an equation involves powers of different bases, it is often clearer to convert both sides of an equation to the same base for simplification. If your friend changed bases from 4 to 16, it definitely should have been correctly justified, especially if those bases relate to exponents being added or subtracted.
2. **Handling exponents**:
- If 16 was changed to \(4^2\), this means that the exponent should have been distributed to any other terms in the equation according to the rules of exponents (i.e., \( (a^m)^n = a^{m \cdot n} \)).
- It's crucial to keep track of exponents when one side of an equation is manipulated compared to the other.
3. **Distribution of exponents**:
- If during simplification or manipulation, the exponents on one side were not properly distributed through the equation, this could lead to an incorrect result.
Considering your friend made specific claims about the correctness of each step, we can break down the answer options:
- "Yes, this is correct. No error was made." — This can only be true if all the manipulation and steps were correct, which needs verification.
- "No, the bases of 4 and 16 should have both been changed to a base of 2." — This is a valid assertion, as it is often easier to work in a common base.
- "No, in step 1 when the 16 changed to 4, it should have been \(4^2\) and the 2 distributed to the current exponent." — If the exponent was not handled correctly, then this would indeed be a crucial error.
- "No, in step 2, the 4 should have been distributed to the current exponents. This would change the equation and yield a different final answer." — Failing to distribute correctly can certainly lead to different outcomes.
Conclusively, without the exact expressions and logical steps provided, it’s difficult to definitively state which of your friend’s arguments holds true in your specific calculation. However, care must always be taken when manipulating exponents and changing bases in any equations.
If you would like to share the specific problem you were trying to solve, I'd be happy to give you a clearer answer!