Question

Match the equation with its solution.

3i+2i−4=18i

2i+3=2i−5

3(2i−7)=6i−21

Answer 1

Let's analyze each equation and solve them step by step to find out which solution corresponds to which equation.

1. **Equation 1**: \( 3i + 2i - 4 = 18i \)

Combine the like terms on the left:
\[
5i - 4 = 18i
\]

Now, isolate \( i \) by bringing \( 18i \) to the left:
\[
5i - 18i = 4
\]
\[
-13i = 4
\]

Therefore:
\[
i = -\frac{4}{13}
\]

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

Subtract \( 2i \) from both sides:
\[
3 = -5
\]

This is a contradiction (not true), meaning there is no solution (inconsistent equation).

3. **Equation 3**: \( 3(2i - 7) = 6i - 21 \)

Distribute the \( 3 \) on the left side:
\[
6i - 21 = 6i - 21
\]

This simplifies to the identity \( 0 = 0 \), which means this equation is true for all \( i \) (infinitely many solutions).

Now, we summarize the results:

- \( 3i + 2i - 4 = 18i \) has the solution: \( i = -\frac{4}{13} \)
- \( 2i + 3 = 2i - 5 \) has no solution (inconsistent).
- \( 3(2i - 7) = 6i - 21 \) is true for all \( i \) (infinitely many solutions).

Matching the equations with their solutions:

- **First equation**: \( i = -\frac{4}{13} \)
- **Second equation**: No solution
- **Third equation**: Infinitely many solutions

Let me know if you need further assistance!