Inline Dropdown 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
because the original equation has
.
The student solved the equation because the original equation has the same solution.
Inline Dropdown 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
because the original equation has
.
correctly
incorrectly
no solution
one solustion
infinitely many solutions
The student solved the equation
incorrectly
because the original equation has
no solution.
The student solved the equation because the original equation has been simplified correctly.
The student solved the equation because the original equation has been simplified.
To determine the missing information in the statement, we need to analyze the steps taken by the student to solve the equation.
Let's break it down step by step:
1. Original equation: 1/4(8-12x) = x - 2(2x + 1)
2. Distribute the 1/4 to both terms inside the parentheses: 2 - 3x = x - 4x + 2
3. Combine like terms on the right side: 2 - 3x = -3x + 2
4. Add 3x to both sides to isolate the x term: 2 - 3x + 3x = -3x + 3x + 2
5. Simplify: 2 = 2
From the steps above, we can see that the student simplified the original equation by performing various operations (distributing, combining like terms, and isolating the x term).
Now, we need to determine what was missing in the original equation. Looking at the steps, we can see that the original equation was missing the distribution step. In line 2, the student performed the distribution by applying the distributive property to both terms inside the parentheses.
Therefore, the statement can be completed as follows:
"The student solved the equation because the original equation has been simplified by distributing on both sides."