Question

Question
Match the equation with its solution(s).
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 - 7 = 18
3 (2i - 7) = 15
3i + 5 = 2i - 7
3i + 5 = 31 + 7
3 (2i + 7) = 6i + 21

Answer 1

To match each equation with its solution(s), we need to first solve each equation step by step.

1. **Equation:** \( 3i + 2i - 7 = 18 \)
- Combine like terms: \( 5i - 7 = 18 \)
- Add 7 to both sides: \( 5i = 25 \)
- Divide by 5: \( i = 5 \)

2. **Equation:** \( 3(2i - 7) = 15 \)
- Expand the left side: \( 6i - 21 = 15 \)
- Add 21 to both sides: \( 6i = 36 \)
- Divide by 6: \( i = 6 \)

3. **Equation:** \( 3i + 5 = 2i - 7 \)
- Subtract \( 2i \) from both sides: \( i + 5 = -7 \)
- Subtract 5 from both sides: \( i = -12 \)

4. **Equation:** \( 3i + 5 = 31 + 7 \)
- Simplify the right side: \( 3i + 5 = 38 \)
- Subtract 5 from both sides: \( 3i = 33 \)
- Divide by 3: \( i = 11 \)

5. **Equation:** \( 3(2i + 7) = 6i + 21 \)
- Expand the left side: \( 6i + 21 = 6i + 21 \)
- This is an identity, meaning it is true for all \( i \).

Now, we can summarize:
- **Equation** \( 3i + 2i - 7 = 18 \) has the **solution** \( i = 5 \).
- **Equation** \( 3(2i - 7) = 15 \) has the **solution** \( i = 6 \).
- **Equation** \( 3i + 5 = 2i - 7 \) has the **solution** \( i = -12 \).
- **Equation** \( 3i + 5 = 31 + 7 \) has the **solution** \( i = 11 \).
- **Equation** \( 3(2i + 7) = 6i + 21 \) is **true for all \( i \)**.

With this, please place the responses in the correct input fields as per the matching.