Match the equation with its solution(s).

Question

3i + 5 = 2i - 7 ____________
3i + 2i - 7 = 18 ____________
3(2i - 7) = 15 _____________
3i + 5 = 3i + 7 _____________
3(2i + 7) = 6i + 21 ____________
Options: i = 7, infinite solutions, i = -12, no solution, i = 5, i = 11, i = 6, i = 2
Fill In The Blanks

Answer 1

Let's solve each equation step-by-step and match them with their respective solutions.

1. Equation: \(3i + 5 = 2i - 7\)
   Solution:
   \(3i - 2i = -7 - 5\)
   \(i = -12\)
   Match: \(3i + 5 = 2i - 7 \) ____________ i = -12

2. Equation: \(3i + 2i - 7 = 18\)
   Solution:
   \(5i - 7 = 18\)
   \(5i = 25\)
   \(i = 5\)
   Match: \(3i + 2i - 7 = 18\) ____________ i = 5

3. Equation: \(3(2i - 7) = 15\)
   Solution:
   \(6i - 21 = 15\)
   \(6i = 36\)
   \(i = 6\)
   Match: \(3(2i - 7) = 15\) _____________ i = 6

4. Equation: \(3i + 5 = 3i + 7\)
   Solution:
   \(5 \neq 7\) ( This is always false)
   Match: \(3i + 5 = 3i + 7\) _____________ no solution

5. Equation: \(3(2i + 7) = 6i + 21\)
   Solution:
   \(6i + 21 = 6i + 21\) (This is always true)
   Match: \(3(2i + 7) = 6i + 21\) ____________ infinite solutions

Now, filling in the blanks completely:

1. \(3i + 5 = 2i - 7 \) ____________ i = -12
2. \(3i + 2i - 7 = 18 \) ____________ i = 5
3. \(3(2i - 7) = 15 \) _____________ i = 6
4. \(3i + 5 = 3i + 7\) _____________ no solution
5. \(3(2i + 7) = 6i + 21\) ____________ infinite solutions

Answer 2

are you sure this is correct

Answer 3

Let's double-check the solutions step-by-step to ensure accuracy for each equation.

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

   • Move \(2i\) to the left side and \(5\) to the right:
     \(3i - 2i = -7 - 5\)
     \(i = -12\)
     Match: \(3i + 5 = 2i - 7 \) → i = -12

2. Equation: \(3i + 2i - 7 = 18\)

   • Combine like terms:
     \(5i - 7 = 18\)
   • Add \(7\) to both sides:
     \(5i = 25\)
   • Divide by \(5\):
     \(i = 5\)
     Match: \(3i + 2i - 7 = 18 \) → i = 5

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

   • Distribute:
     \(6i - 21 = 15\)
   • Add \(21\) to both sides:
     \(6i = 36\)
   • Divide by \(6\):
     \(i = 6\)
     Match: \(3(2i - 7) = 15 \) → i = 6

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

   • Subtract \(3i\) from both sides:
     \(5 = 7\) (This is always false)
     Match: \(3i + 5 = 3i + 7\) → no solution

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

   • Distribute on the left:
     \(6i + 21 = 6i + 21\) (This is always true)
     Match: \(3(2i + 7) = 6i + 21\) → infinite solutions

Summary of Matches:

1. \(3i + 5 = 2i - 7 \) → i = -12
2. \(3i + 2i - 7 = 18 \) → i = 5
3. \(3(2i - 7) = 15 \) → i = 6
4. \(3i + 5 = 3i + 7\) → no solution
5. \(3(2i + 7) = 6i + 21\) → infinite solutions

Everything previously stated is indeed confirmed to be correct. Thank you for the opportunity to verify!