3. A student solved the following equation using the following steps:
4(2−3x)=x−2(2x+1)
8−3x=x−4x−2
8−3x=−3x−2
No solution.
(2 points)
Based on the student's work, the equation was solved
incorrectly
The equation solved correctly would show that it has
solution(s).
Based on the student's work, the equation was solved incorrectly. The correct solution should show that the equation has solution(s).
3. A student solved the following equation using the following steps:
4(2−3x)=x−2(2x+1)
8−3x=x−4x−2
8−3x=−3x−2
No solution.
(2 points)
Based on the student's work, the equation was solved
incorrectly
The equation solved correctly would show that it has
solution(s).
Based on the student's work, the equation was solved incorrectly. The correct solution would show that the equation has solution(s). In this case, the student obtained the equation 8 - 3x = -3x - 2, which leads to the conclusion that there is no solution. However, there is an error in the steps taken by the student. Specifically, there is an error in the step where they subtracted x from both sides of the equation. This step should have resulted in 8 - 3x = -3x - 1, not 8 - 3x = -3x - 2. Therefore, if the equation was solved correctly, it should have shown that it has solution(s).
The equation solved correctly would show that it has
solution(s
The equation solved correctly would indeed show that it has solution(s). In this case, the student made an error in their solution, leading to the incorrect conclusion that there is no solution. However, if the student had correctly solved the equation, it should have shown that there are solutions to the equation.
4. Select the equation that has infinitely many solutions.(1 point)
Responses
3x=2x+1
3 x is equal to 2 x plus 1
4x+1=4(x+1)
4 x plus 1 is equal to 4 times open paren x plus 1 close paren
3−3x=−3(x−1)
3 minus 3 x is equal to negative 3 times open paren x minus 1 close paren
3x+5=3x−5
The equation that has infinitely many solutions is:
3x = 2x + 1
5. A student solved the following equation using the following steps:
2(2x+2)=4(x+4)
4x+4=4x+4
4=4
Infinitely many solutions
(2 points)
Based on the student's work, the equation was solved
The equation solved correctly would show that it has
solution(s).