Let's analyze the student's steps to determine if they accurately solved the equation and what the solution indicates.
The original equation they intended to solve is:
\[ 4(2 - 3x) = x - 2(2x + 1) \]
- Distributing both sides:
- Left side: \( 4(2 - 3x) = 8 - 12x \)
- Right side: \( x - 2(2x + 1) = x - 4x - 2 = -3x - 2 \)
So we rewrite the equation:
\[ 8 - 12x = -3x - 2 \]
-
Reorganizing it as the student did:
- This was done correctly as follows:
\[ 8 - 12x = -3x - 2 \]
-
Moving all terms involving \( x \) to one side:
- After looking at the student's next step, it appears they did some simplification or reorganization but ended up repeating an incorrect format. Let's set it properly:
\[ 8 - 12x = -3x - 2 \]
Now, adding \( 12x \) to both sides and \( 2 \) to both sides gives:
\[ 8 + 2 = 12x - 3x \] \[ 10 = 9x \]
Therefore, solving for \( x \): \[ x = \frac{10}{9} \]
Conclusion
The final calculation shows there is a solution to the equation, specifically \( x = \frac{10}{9} \).
If the student's final answer states "No Solution," that is incorrect based on this analysis. The original equation indeed has a solution, meaning the student made an error in their simplification steps or reasoning down the line.
The conclusion is that the equation has a solution, and the correct final form of the statement should indicate that the equation solved correctly shows it has one unique solution \( x = \frac{10}{9} \).
1 answer