Question

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

Answer 1

To match the equations with their solutions, let's 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: 3i + 5 = 3i + 7**
- Subtract 3i from both sides:
- 5 = 7 (This is not true, no solution.)

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

4. **Equation: 3(2i + 7) = 6i + 21**
- Distribute:
- 6i + 21 = 6i + 21 (This is always true, infinite solutions.)

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

Now, let’s summarize the solutions:
1. 3i + 2i - 7 = 18 ⟹ i = 5
2. 3i + 5 = 3i + 7 ⟹ No solution
3. 3(2i - 7) = 15 ⟹ i = 6
4. 3(2i + 7) = 6i + 21 ⟹ Infinite solutions
5. 3i + 5 = 2i - 7 ⟹ i = -12

### Final Matching:
- **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)
- **3i + 5 = 2i - 7** → (i = -12)