Question

Match the equation with its solution(s).
3i + 5 = 2i - 7 ____________
3i + 2i - 7 = 18 ____________
3(2i - 7) = 15 _____________
3i + 5 = 3i + 7 _____________
3(2i + 7) = 6i + 21 ____________
Options: i = 7, infinite solutions, i = -12, no solution, i = 5, i = 11, i = 6, i = 2
Fill In The Blanks

Answer 1

are you sure this is correct

Answer 2

Let's solve each equation step-by-step and match them with their respective solutions.

1. **Equation:** \(3i + 5 = 2i - 7\)
**Solution:**
\(3i - 2i = -7 - 5\)
\(i = -12\)
**Match:** \(3i + 5 = 2i - 7 \) ____________ **i = -12**

2. **Equation:** \(3i + 2i - 7 = 18\)
**Solution:**
\(5i - 7 = 18\)
\(5i = 25\)
\(i = 5\)
**Match:** \(3i + 2i - 7 = 18\) ____________ **i = 5**

3. **Equation:** \(3(2i - 7) = 15\)
**Solution:**
\(6i - 21 = 15\)
\(6i = 36\)
\(i = 6\)
**Match:** \(3(2i - 7) = 15\) _____________ **i = 6**

4. **Equation:** \(3i + 5 = 3i + 7\)
**Solution:**
\(5 \neq 7\) ( This is always false)
**Match:** \(3i + 5 = 3i + 7\) _____________ **no solution**

5. **Equation:** \(3(2i + 7) = 6i + 21\)
**Solution:**
\(6i + 21 = 6i + 21\) (This is always true)
**Match:** \(3(2i + 7) = 6i + 21\) ____________ **infinite solutions**

Now, filling in the blanks completely:

1. \(3i + 5 = 2i - 7 \) ____________ **i = -12**
2. \(3i + 2i - 7 = 18 \) ____________ **i = 5**
3. \(3(2i - 7) = 15 \) _____________ **i = 6**
4. \(3i + 5 = 3i + 7\) _____________ **no solution**
5. \(3(2i + 7) = 6i + 21\) ____________ **infinite solutions**

Answer 3

Let's double-check the solutions step-by-step to ensure accuracy for each equation.

1. **Equation:** \(3i + 5 = 2i - 7\)
- Move \(2i\) to the left side and \(5\) to the right:
\(3i - 2i = -7 - 5\)
\(i = -12\)
**Match:** \(3i + 5 = 2i - 7 \) → **i = -12**

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

3. **Equation:** \(3(2i - 7) = 15\)
- Distribute:
\(6i - 21 = 15\)
- Add \(21\) to both sides:
\(6i = 36\)
- Divide by \(6\):
\(i = 6\)
**Match:** \(3(2i - 7) = 15 \) → **i = 6**

4. **Equation:** \(3i + 5 = 3i + 7\)
- Subtract \(3i\) from both sides:
\(5 = 7\) (This is always false)
**Match:** \(3i + 5 = 3i + 7\) → **no solution**

5. **Equation:** \(3(2i + 7) = 6i + 21\)
- Distribute on the left:
\(6i + 21 = 6i + 21\) (This is always true)
**Match:** \(3(2i + 7) = 6i + 21\) → **infinite solutions**

### Summary of Matches:
1. \(3i + 5 = 2i - 7 \) → **i = -12**
2. \(3i + 2i - 7 = 18 \) → **i = 5**
3. \(3(2i - 7) = 15 \) → **i = 6**
4. \(3i + 5 = 3i + 7\) → **no solution**
5. \(3(2i + 7) = 6i + 21\) → **infinite solutions**

Everything previously stated is indeed confirmed to be correct. Thank you for the opportunity to verify!