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Match the equation with its solution(s).(5 points)

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3i+2i−7=18
3(2i+7)=6i+21
3i+5=3i+7
3(2i−7)=15
3i+5=2i−7

1 answer

To match each equation with its solution, we will 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: \( 3(2i + 7) = 6i + 21 \)

    • Distribute on the left: \( 6i + 21 = 6i + 21 \)
    • This is an identity; it has infinitely many solutions (or could be considered as every \( i \) is a solution).

  3. Equation: \( 3i + 5 = 3i + 7 \)

    • Subtract \( 3i \) from both sides: \( 5 = 7 \)
    • This statement is false, so there are no solutions.

  4. Equation: \( 3(2i - 7) = 15 \)

    • Distribute on the left: \( 6i - 21 = 15 \)
    • Add 21 to both sides: \( 6i = 36 \)
    • Divide by 6: \( i = 6 \)

  5. Equation: \( 3i + 5 = 2i - 7 \)

    • Subtract \( 2i \) from both sides: \( i + 5 = -7 \)
    • Subtract 5 from both sides: \( i = -12 \)

Now matching each equation with its solution:

  • \( 3i + 2i - 7 = 18 \) → \( i = 5 \)
  • \( 3(2i + 7) = 6i + 21 \) → infinitely many solutions
  • \( 3i + 5 = 3i + 7 \) → no solutions
  • \( 3(2i - 7) = 15 \) → \( i = 6 \)
  • \( 3i + 5 = 2i - 7 \) → \( i = -12 \)

So the completed matches are:

  • \( 3i + 2i - 7 = 18 \) → \( i = 5 \)
  • \( 3(2i + 7) = 6i + 21 \) → infinitely many solutions
  • \( 3i + 5 = 3i + 7 \) → no solutions
  • \( 3(2i - 7) = 15 \) → \( i = 6 \)
  • \( 3i + 5 = 2i - 7 \) → \( i = -12 \)