Ask a New Question
Menu

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

A student solved an equation, as shown below. 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 .

3 answers

Let's analyze the student's work step by step to fill in the gaps in the statement.

  1. The first equation is: \[ \frac{1}{4}(8-12x) = x - 2(2x + 1) \] The student distributes and simplifies this equation correctly to find \(x\).

  2. The subsequent equations show the student is trying to manipulate the equation around to isolate variables but ultimately shows that the equation reduces to: \[ 2 = 2 \] This means the equation is always true, indicating that it is an identity.

Based on this analysis, the statements can be completed as follows:

The student solved the equation as an identity because the original equation has infinite solutions or all real numbers as solutions.

Here’s how the final completed statement could look: "The student solved the equation as an identity because the original equation has infinite solutions."

correct? incorrect?

The assessment in my previous response was correct. The student solved the equation as an identity because the original equation simplifies to \(2 = 2\), which holds true for any value of \(x\). This indicates that the equation has infinite solutions (or all real numbers as solutions).

Therefore, the answer is correct.

If we summarize it simply, you would say:

The student solved the equation as an identity because the original equation has infinite solutions.

Feel free to ask if you need additional clarification or assistance!