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Match the equation with its solution(s).
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3i + 2i - 7 = 18
3 (2i - 7) = 15
3i + 5 = 2i - 7
3i + 5 = 31 + 7
3 (2i + 7) = 6i + 21

1 answer

To match each equation with its solution(s), we need to first 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: \( 3(2i - 7) = 15 \)

    • Expand the left side: \( 6i - 21 = 15 \)
    • 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: \( 3i + 5 = 31 + 7 \)

    • Simplify the right side: \( 3i + 5 = 38 \)
    • Subtract 5 from both sides: \( 3i = 33 \)
    • Divide by 3: \( i = 11 \)

  5. Equation: \( 3(2i + 7) = 6i + 21 \)

    • Expand the left side: \( 6i + 21 = 6i + 21 \)
    • This is an identity, meaning it is true for all \( i \).

Now, we can summarize:

  • Equation \( 3i + 2i - 7 = 18 \) has the solution \( i = 5 \).
  • Equation \( 3(2i - 7) = 15 \) has the solution \( i = 6 \).
  • Equation \( 3i + 5 = 2i - 7 \) has the solution \( i = -12 \).
  • Equation \( 3i + 5 = 31 + 7 \) has the solution \( i = 11 \).
  • Equation \( 3(2i + 7) = 6i + 21 \) is true for all \( i \).

With this, please place the responses in the correct input fields as per the matching.