Question

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

Answer 1

Let's solve each of the equations step by step and find their solutions:

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:** \( 3(2i - 7) = 15 \)
- Distribute: \( 6i - 21 = 15 \)
- 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:** \( 3i + 5 = 3i + 7 \)
- Subtract \( 3i \) from both sides: \( 5 = 7 \)
- This is a contradiction (no solution).

5. **Equation:** \( 3(2i + 7) = 6i + 21 \)
- Distribute: \( 6i + 21 = 6i + 21 \)
- This identity holds for all \( i \) (infinitely many solutions).

Now we can match the equations with their solutions:

1. **\( 3i + 2i - 7 = 18 \)** → **\( i = 5 \)**
2. **\( 3(2i - 7) = 15 \)** → **\( i = 6 \)**
3. **\( 3i + 5 = 2i - 7 \)** → **\( i = -12 \)**
4. **\( 3i + 5 = 3i + 7 \)** → **No solution**
5. **\( 3(2i + 7) = 6i + 21 \)** → **Infinitely many solutions**

This completes the matching of the equations with their respective solutions.