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-
3 answers
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.
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.
