A student solved an equation, as shown below.

Question

The first line shows 1 over 4 left Parenthesis 8 minus 12x right parenthesis equals x minus 2 left parenthesis 2x plus 1 right parenthesis, second line shows 2 minus 3x equals x minus 4x plus 2, third line shows 2 minus 3x equals 3x plus 2, fourth line shows 2 minus 3x plus 3x equals negative 3x plus 3x plus 2. Fifth line shows 2 equals 2.

Based on the student's work, complete the statement below.

Use the drop-down menus to make the statement below true.

The student solved the equation Query 1
because the original equation has Query 2.

responces Query 1:
Correctly
Incorrectly

responces Query 2:
No solution
One solution
Infinitely many solutions

Answer 1

Based on the student's work, we can analyze the steps taken in solving the equation:

1. The initial equation is \( \frac{1}{4}(8 - 12x) = x - 2(2x + 1) \).
2. The steps lead to the statement \( 2 = 2 \), which is a true statement and indicates that the left side and right side are equal regardless of the value of \( x \).

This shows that the original equation simplifies down to a true statement for all values of \( x \), which means the equation has infinitely many solutions.

Therefore, the correct completion of the statement is:

The student solved the equation Correctly because the original equation has Infinitely many solutions.