Question
When solving the problem 5x+4=53x−2, your friend does the following: 5(x)+4=5(3x)−2 5x+4=15x−2 6=10x x=35 Was this correct? Responses This is not correct. When the bases are the same, we can drop the bases and set the exponents equal to each other and solve that equation. This is not correct. When the bases are the same, we can drop the bases and set the exponents equal to each other and solve that equation. This is not correct. Both sides should be divided by 5 instead of multiplied by 5. This is not correct. Both sides should be divided by 5 instead of multiplied by 5. Yes, this is correct. No error was made. Yes, this is correct. No error was made. This is not correct. The 5 needs to be distributed across all terms when solving.
Answers
GPT-4o mini
Let's analyze your friend's solution step by step to see where the error was made.
1. Your friend starts with the equation:
\[
5x + 4 = 53x - 2
\]
2. They rewrite the equation incorrectly as:
\[
5(x) + 4 = 5(3x) - 2
\]
This step is incorrect. The left side is correct, but they fumbled the right side; it should remain \(53x\), not \(5(3x)\).
3. They then incorrectly simplify this to:
\[
5x + 4 = 15x - 2
\]
This is wrong because of the earlier mistake.
4. Then they follow through with:
\[
5x + 4 = 15x - 2
\]
If we were to continue from the previous wrong equation.
5. They combine like terms and attempt to solve for \(x\):
\[
4 + 2 = 15x - 5x
\]
Which simplifies incorrectly to:
\[
6 = 10x
\]
and gives \(x = \frac{6}{10} = \frac{3}{5}\) instead of \(x = \frac{35}{5}\).
So, the conclusion is that your friend's solution contains multiple errors, starting from the incorrect rewriting of the equation.
Therefore, the correct response would be:
"This is not correct. They rewrote the equation incorrectly and made several mistakes in the process."
1. Your friend starts with the equation:
\[
5x + 4 = 53x - 2
\]
2. They rewrite the equation incorrectly as:
\[
5(x) + 4 = 5(3x) - 2
\]
This step is incorrect. The left side is correct, but they fumbled the right side; it should remain \(53x\), not \(5(3x)\).
3. They then incorrectly simplify this to:
\[
5x + 4 = 15x - 2
\]
This is wrong because of the earlier mistake.
4. Then they follow through with:
\[
5x + 4 = 15x - 2
\]
If we were to continue from the previous wrong equation.
5. They combine like terms and attempt to solve for \(x\):
\[
4 + 2 = 15x - 5x
\]
Which simplifies incorrectly to:
\[
6 = 10x
\]
and gives \(x = \frac{6}{10} = \frac{3}{5}\) instead of \(x = \frac{35}{5}\).
So, the conclusion is that your friend's solution contains multiple errors, starting from the incorrect rewriting of the equation.
Therefore, the correct response would be:
"This is not correct. They rewrote the equation incorrectly and made several mistakes in the process."