Question

A student solved an equation, as shown below.
1/4 (8-12x)=x-2(2x+1)
2-3x=x-4x+2
2-3x=-3x+2
2-3x+3x=-3x+3x+2
2=2
Based on the student's work, complete the statement below. The student solved the equation -Blank 1- because the original equation has -Blank 2-

Answer 1

blank needs to be a single answer what do I choose?

Answer 2

Based on the student's work, we can infer the following:

**Blank 1:** "correctly"

**Blank 2:** "infinite solutions" or "no solution"

Explanation:
The step where the student arrived at "2 = 2" indicates that the equation simplifies to a true statement for all values of \(x\). This means that the original equation is an identity, implying that it has infinitely many solutions.

Answer 3

For a single answer, you can choose:

**Blank 1:** "correctly"

**Blank 2:** "infinitely many solutions"

So the completed statement would read:

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