Question

3. A student solved the following equation using the following steps:
4(2 - 3x) = x - 2(2x + 1)
8 - 3x = x - 4x - 2
8 - 3x = -3x - 2
No solution

1. Based on the student's work, the equation was solved blank.
2. The equation solved correctly would show that it has blank solution(s).
Fill in the blanks.

Answer 1

1. Based on the student's work, the equation was solved incorrectly.
2. The equation solved correctly would show that it has one solution.

Here's a brief explanation:

The student's steps lead to a point where both sides are equivalent (\(8 - 3x = -3x - 2\)), but they didn’t proceed correctly to find the solution. Solving the equation properly:

Starting from \(4(2 - 3x) = x - 2(2x + 1)\):
1. Expand both sides:
\(8 - 12x = x - 4x - 2\)
Which simplifies to:
\(8 - 12x = -3x - 2\)

2. Rearranging gives:
\(8 + 2 = -3x + 12x\)
\(10 = 9x\)

3. Thus, \(x = \frac{10}{9}\).

So the equation has one solution.