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.

(2 points)
Based on the student's work, the equation was solved

The equation solved correctly would show that it has
solution(s).

Answer 1

Let's methodically analyze the student's steps, starting with the initial equation:

1. Original Equation: \(4(2 - 3x) = x - 2(2x + 1)\)

Now let's break it down step by step:

2. Distributing on both sides:

   Left Side: \[ 4(2 - 3x) = 8 - 12x \]

   Right Side: \[ x - 2(2x + 1) = x - (4x + 2) = x - 4x - 2 = -3x - 2 \]

   So now we have: \[ 8 - 12x = -3x - 2 \]

3. Simplifying: Now we need to solve for \(x\).

   Rearranging the equation gives: \[ 8 + 2 = -3x + 12x \] \[ 10 = 9x \] \[ x = \frac{10}{9} \]

Conclusion

The student's conclusion of "No solution" is incorrect. Based on the correct manipulations, the original equation has one solution:

\[ x = \frac{10}{9} \]

Thus, it shows that the equation has 1 solution.