Question
When solving the problem 7x+2=73x−8 , your friend does the following: 7(x)+2=7(3x)−8 7x+2=21x−8 10=14x x=57 Was this correct? (1 point) Responses This is not correct. Both sides should be divided by 7 instead of multiplied by 7. This is not correct. Both sides should be divided by 7 instead of multiplied by 7. This is not correct. When the bases are the same, then we can set the exponents equal to each other and solve that equation. This is not correct. When the bases are the same, then we can set the exponents equal to each other and solve that equation. This is not correct. The 7 needs to be distributed across all terms when solving. This is not correct. The 7 needs to be distributed across all terms when solving. Yes, this is correct. No error was made. Yes, this is correct. No error was made.
Answers
GPT-4o mini
Your friend's solution contains errors. Let's go through the steps taken to solve the equation \(7x + 2 = 73x - 8\).
1. **Rewrite the equation**: The original equation is \(7x + 2 = 73x - 8\).
2. **Combine like terms**: To solve for \(x\), we want to get all the \(x\) terms on one side and the constant terms on the other side. We can do this by subtracting \(7x\) from both sides:
\[
2 = 73x - 7x - 8
\]
which simplifies to:
\[
2 = 66x - 8
\]
3. **Add 8 to both sides to isolate the term with \(x\)**:
\[
2 + 8 = 66x
\]
\[
10 = 66x
\]
4. **Divide both sides by 66 to solve for \(x\)**:
\[
x = \frac{10}{66} = \frac{5}{33}
\]
Your friend's approach included multiplying both sides by 7 incorrectly and interpreting \(73x\) as \(7(3x)\), which led to faulty steps. Therefore, their final answer \(x = 57\) is not correct.
The correct response here is: "This is not correct. Both sides should be divided by 66 instead of being misinterpreted or multiplied by 7."
1. **Rewrite the equation**: The original equation is \(7x + 2 = 73x - 8\).
2. **Combine like terms**: To solve for \(x\), we want to get all the \(x\) terms on one side and the constant terms on the other side. We can do this by subtracting \(7x\) from both sides:
\[
2 = 73x - 7x - 8
\]
which simplifies to:
\[
2 = 66x - 8
\]
3. **Add 8 to both sides to isolate the term with \(x\)**:
\[
2 + 8 = 66x
\]
\[
10 = 66x
\]
4. **Divide both sides by 66 to solve for \(x\)**:
\[
x = \frac{10}{66} = \frac{5}{33}
\]
Your friend's approach included multiplying both sides by 7 incorrectly and interpreting \(73x\) as \(7(3x)\), which led to faulty steps. Therefore, their final answer \(x = 57\) is not correct.
The correct response here is: "This is not correct. Both sides should be divided by 66 instead of being misinterpreted or multiplied by 7."