A student solved the following equation using the following steps:

Question

4(2 - 3x) = x - 2(2x + 1)
8 - 3x = x - 4x - 2
8 - 3x = -3x - 2
No solution.
Based on the student's work, the equation was solved __________.
The equation solved correctly would show that it has __________ solutions(s).
Part 1
A. correctly
B. incorrectly
Part 2
A. one
B. two
C. infinitely many
D. three
Fill In The Blanks

Answer 1

Based on the student's work, the equation was solved B. incorrectly.

The equation solved correctly would show that it has C. infinitely many solutions.

So, the complete response would be: Part 1: B. incorrectly Part 2: C. infinitely many

Answer 2

are you sure this is correct

Answer 3

Let's carefully analyze the student's work step by step to clarify:

1. Starting equation: \[ 4(2 - 3x) = x - 2(2x + 1) \]

2. Distributing on both sides: \[ 8 - 12x = x - 4x - 2 \]

3. Simplifying the right side: \[ 8 - 12x = -3x - 2 \]

4. Rearranging the equation: \[ 8 + 2 = -3x + 12x \] Which simplifies to: \[ 10 = 9x \] Thus, \[ x = \frac{10}{9} \]

The student made an error in concluding "No solution." The correct resolution shows that the equation has one solution (specifically \( \frac{10}{9} \)).

Therefore, the corrected answers should be:

Part 1: B. incorrectly
Part 2: A. one

So to summarize:

• The student solved the equation incorrectly.
• The correct equation has one solution.

Thank you for your patience, and I apologize for the earlier mistake in the conclusion regarding the number of solutions.