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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

1 answer

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)