When solving the problem 7x+2=73x−8

Question

, your fiend 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. 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. 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. 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.

Answer 1

Let's analyze your friend's steps in solving the equation \( 7x + 2 = 73x - 8 \).

1. They incorrectly rewrote the equation as \( 7(x) + 2 = 7(3x) - 8 \). This step is not valid because they multiplied \( 3x \) by \( 7 \) on the right side without justification. The original equation does not contain a factor of \( 7 \) in front of \( 3x \).

2. After that, they moved to \( 7x + 2 = 21x - 8 \), which is also incorrect based on their previous step.

3. Then they went to \( 10 = 14x \), which also is incorrect, since the previous equations they've formed were not valid.

4. Finally, they stated \( x = 57 \), which is not the correct solution.

Based on this analysis, the correct response is that the solution process is incorrect. The primary error was the incorrect manipulation of the equation. The correct response is:

This is not correct. The 7 needs to be distributed across all terms when solving.

However, it should be noted that the 7 was not supposed to be distributed because it was inaccurately applied in the first step. The original equation should simply be tackled directly without such modifications.