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

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. 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.

Answer 1

Let's analyze your friend's work step-by-step:

Starting with the original equation:

\[ 7x + 2 = 73x - 8 \]

Your friend rewrote it as:

\[ 7(x) + 2 = 7(3x) - 8 \]

From that point, they correctly distributed the terms:

\[ 7x + 2 = 21x - 8 \]

Next, the friend moves all terms involving \( x \) to one side and constants to the other side:

This step appears to be where the error occurs. They should have rearranged the equation as follows:

1. Move the \( 21x \) to the left side:

\[ 7x - 21x + 2 = -8 \]

This leads to:

\[ -14x + 2 = -8 \]

2. Next, move the \( 2 \) to the right side:

\[ -14x = -8 - 2 \]

Thus:

\[ -14x = -10 \]

3. Now, divide by \(-14\) to solve for \( x \):

\[ x = \frac{10}{14} = \frac{5}{7} \]

Therefore, your friend's solution is incorrect.

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

The specific issue is that they correctly distributed the \( 7 \) but made an arithmetic error in subsequent steps, leading to the incorrect value for \( x \).