Question

A student solved an equation, as shown below.
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

Answer 1

To complete the statement based on the student's work, we can analyze the steps and the final outcome.

1. **Query 1:** The student solved the equation **correctly**. (This is because the final statement "2 = 2" indicates that the equation is true for all values of x).

2. **Query 2:** The original equation has **infinitely many solutions**. (Since the equation simplifies to a true statement that is always valid, it shows that there are infinitely many values of x that satisfy the equation).

Putting it all together, the completed statement is:

The student solved the equation **correctly** because the original equation has **infinitely many solutions**.