Let's analyze the student's work step by step to see if the equation was solved correctly and determine the number of solutions.
The original equation is:
\[ 4(2 - 3x) = x - 2(2x + 1) \]
Step 1: Distribute both sides.
On the left side:
\[ 4(2 - 3x) = 8 - 12x \]
On the right side:
\[ x - 2(2x + 1) = x - 4x - 2 = -3x - 2 \]
So we rewrite the equation as:
\[ 8 - 12x = -3x - 2 \]
Step 2: Now, rearranging the equation to combine like terms.
The student's next step is:
\[ 8 - 3x = -3x - 2 \]
This seems to be incorrect because it doesn't match with our calculations above. The correct form is:
\[ 8 - 12x = -3x - 2 \]
Step 3: Let's solve it correctly:
Add \(3x\) to both sides:
\[ 8 - 12x + 3x = -2 \]
Which simplifies to:
\[ 8 - 9x = -2 \]
Now subtract 8 from both sides:
\[ -9x = -10 \]
Now divide by -9:
\[ x = \frac{10}{9} \]
Conclusion:
The original student claim stated "No solution" is incorrect. The correctly solved equation shows that it has one solution, namely \( x = \frac{10}{9} \).
So, the equation has one solution.