Question
1 of 51 of 5 Items
Question 1
1. Match the equation with its solution.(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
3i+2i−4=18i
3(2i−7)=6i−21
2i+3=2i−5
Question 2
2. Look at the steps for solving the equation and choose a true statement.
3x−9x+1=2(−3x+1)−1
−6x+1=−6x+2−1
−6x+1=−6x+1
(1 point)
Responses
The only solution to the equation is -6
The only solution to the equation is -6
The only solution to the equation is 1
The only solution to the equation is 1
There are infinitely many solutions to the equation.
There are infinitely many solutions to the equation.
There is no way to know if there is a solution to the equation.
There is no way to know if there is a solution to the equation.
There are no solutions to the equation.
There are no solutions to the equation.
Question 3
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
The equation solved correctly would show that it has
solution(s).
Question 4
4. Select the equation that has infinitely many solutions.(1 point)
Responses
3x+5=3x−5
3 x plus 5 is equal to 3 x minus 5
3−3x=−3(x−1)
3 minus 3 x is equal to negative 3 times open paren x minus 1 close paren
4x+1=4(x+1)
4 x plus 1 is equal to 4 times open paren x plus 1 close paren
3x=2x+1
3 x is equal to 2 x plus 1
Question 5
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).
Answers
GPT-4o mini
Here are the answers and explanations for each question:
### Question 1:
**Match the equation with its solution:**
1. **3i + 2i - 4 = 18i** → This simplifies to \(5i - 4 = 18i\), leading to the solution \(i = -\frac{4}{13}\), which is technically a solution but will need to look for the exact breakdown.
2. **3(2i - 7) = 6i - 21** → This simplifies correctly to \(6i - 21 = 6i - 21\), which indicates infinitely many solutions.
3. **2i + 3 = 2i - 5** → This leads to \(3 = -5\), which is not possible, hence no solutions.
### Question 2:
**True statement regarding the steps for the equation:**
- The statement **"There are infinitely many solutions to the equation."** is true since both sides simplify to \(1 = 1\).
### Question 3:
**Based on the student's work:**
- The conclusion that "No solution" indicates an error in understanding. The student arrived at a false statement \(8 - 3x = -3x - 2\) which needs to be clarified. The equation simplifies, but in this case, you'd find it would yield no possible x if done correctly, though it's worth noting that when the simplified steps yield the same format without contradictions would indicate infinitely many solutions, not no solution.
### Question 4:
**Select the equation that has infinitely many solutions:**
- **3x + 5 = 3x - 5** is the correct answer, as it simplifies to \(5 = -5\), which is a contradiction, indicating no solutions.
- The equation **3 − 3x = −3(x − 1)** simplifies correctly to \(3 - 3x = -3x + 3\), which holds true.
- Therefore the one indicating infinite solutions would be one that resolves down to a true identity, so this clarification would lead to selecting the **3 − 3x = −3(x − 1)** option as the equation that will yield infinitely many.
### Question 5:
**Based on the student's work:**
- The student concluded **Infinitely many solutions** correctly, as both sides of their equation resulted in identical terms leading to a true statement.
In summary:
- **Question 1**: 3(2i - 7) has infinitely many solutions, the others are individually resolved as per assumption but this needs cross-check with solutions.
- **Question 2**: Infinitely many solutions.
- **Question 3**: Needs more clarification, incorrectly assumed, would conclude from laid out steps.
- **Question 4**: 3 − 3x = −3(x − 1) has infinitely many solutions.
- **Question 5**: Infinitely many solutions accurately stated.
### Question 1:
**Match the equation with its solution:**
1. **3i + 2i - 4 = 18i** → This simplifies to \(5i - 4 = 18i\), leading to the solution \(i = -\frac{4}{13}\), which is technically a solution but will need to look for the exact breakdown.
2. **3(2i - 7) = 6i - 21** → This simplifies correctly to \(6i - 21 = 6i - 21\), which indicates infinitely many solutions.
3. **2i + 3 = 2i - 5** → This leads to \(3 = -5\), which is not possible, hence no solutions.
### Question 2:
**True statement regarding the steps for the equation:**
- The statement **"There are infinitely many solutions to the equation."** is true since both sides simplify to \(1 = 1\).
### Question 3:
**Based on the student's work:**
- The conclusion that "No solution" indicates an error in understanding. The student arrived at a false statement \(8 - 3x = -3x - 2\) which needs to be clarified. The equation simplifies, but in this case, you'd find it would yield no possible x if done correctly, though it's worth noting that when the simplified steps yield the same format without contradictions would indicate infinitely many solutions, not no solution.
### Question 4:
**Select the equation that has infinitely many solutions:**
- **3x + 5 = 3x - 5** is the correct answer, as it simplifies to \(5 = -5\), which is a contradiction, indicating no solutions.
- The equation **3 − 3x = −3(x − 1)** simplifies correctly to \(3 - 3x = -3x + 3\), which holds true.
- Therefore the one indicating infinite solutions would be one that resolves down to a true identity, so this clarification would lead to selecting the **3 − 3x = −3(x − 1)** option as the equation that will yield infinitely many.
### Question 5:
**Based on the student's work:**
- The student concluded **Infinitely many solutions** correctly, as both sides of their equation resulted in identical terms leading to a true statement.
In summary:
- **Question 1**: 3(2i - 7) has infinitely many solutions, the others are individually resolved as per assumption but this needs cross-check with solutions.
- **Question 2**: Infinitely many solutions.
- **Question 3**: Needs more clarification, incorrectly assumed, would conclude from laid out steps.
- **Question 4**: 3 − 3x = −3(x − 1) has infinitely many solutions.
- **Question 5**: Infinitely many solutions accurately stated.