Question

Match the equation with its solution(s)
3i+5=2i−7

3i+2i−7=18

3i+5=3i+7

3(2i−7)=15

3(2i+7)=6i+21

Answer 1

Let's solve each of the equations given and list the corresponding solutions:

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

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

3. **Equation:** \(3i + 5 = 3i + 7\)
**Solution:**
\[ 3i - 3i = 7 - 5 \]
\[ 0 = 2 \] (no solution, contradiction)

4. **Equation:** \(3(2i - 7) = 15\)
**Solution:**
\[ 6i - 21 = 15 \]
\[ 6i = 15 + 21 \]
\[ 6i = 36 \]
\[ i = 6 \]

5. **Equation:** \(3(2i + 7) = 6i + 21\)
**Solution:**
\[ 6i + 21 = 6i + 21 \] (true for all \(i\), infinite solutions)

### Summary of Equations and Solutions
- **\(3i + 5 = 2i - 7\)** ➔ \(i = -12\)
- **\(3i + 2i - 7 = 18\)** ➔ \(i = 5\)
- **\(3i + 5 = 3i + 7\)** ➔ No solution
- **\(3(2i - 7) = 15\)** ➔ \(i = 6\)
- **\(3(2i + 7) = 6i + 21\)** ➔ Infinite solutions

Feel free to ask if you have any further questions or need clarification on any of these steps!