When solving the problem 7x+2=73x−8

Question

7
𝑥
+
2
=
7
3
𝑥
−
8
, your fiend does the following:
7(x)+2=7(3x)−8
7
(
𝑥
)
+
2
=
7
(
3
𝑥
)
−
8
7x+2=21x−8
7
𝑥
+
2
=
21
𝑥
−
8
10=14x
10
=
14
𝑥
x=57
𝑥
=
5
7
Was this correct?
(1 point)
Responses
Yes, this is correct. No error was made.
Yes, this is correct. No error was made.
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.
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.

Answer 1

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

1. The equation given is \( 7x + 2 = 73x - 8 \).
2. The friend incorrectly interprets \( 73x \) to mean \( 7(3x) \), which is incorrect.
3. After that, the steps taken were:
   • They rewrote it as \( 7(x) + 2 = 7(3x) - 8 \), which is incorrect since \( 73x \) should remain as is.
   • They then simplified it to \( 7x + 2 = 21x - 8 \), which is also incorrect as the original term \( 73x \) was not simplified correctly.
4. From there, they attempted to isolate \( x \) and arrived at \( x = \frac{5}{7} \).

Since the critical step of interpreting \( 73x \) incorrectly led to the wrong equation throughout the solution, the final result is indeed incorrect.

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

However, it's important to note that the primary error was the improper interpretation of \( 73x \), and the process from there was flawed as well. The correct approach should indeed maintain \( 73x \) without breaking it down inappropriately.