Question

Match the equation with its solution.
3i + 2i - 4 = 18i ______________
2i + 3 = 2i - 5 _______________
3(2i - 7) = 6i - 21 _____________
Options: Infinite Solutions, i = 8, i = 4/13, i = 5, No Solution

Answer 1

are you sure this is correct

Answer 2

Let's solve each equation one by one and match them with the options given.

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

Combine the terms on the left side:

\[(3i + 2i) - 4 = 18i\]

\[5i - 4 = 18i\]

Now, isolate \(i\):

\[-4 = 18i - 5i\]

\[-4 = 13i\]

Therefore,

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

This does not match any of the options directly, so we will move on.

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

Subtract \(2i\) from both sides:

\[3 = -5\]

This is not true, which indicates:

**No Solution**.

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

Distributing the left side:

\[6i - 21 = 6i - 21\]

This simplifies to an identity, meaning both sides are equal for all values of \(i\):

**Infinite Solutions**.

Now let's compile the matches:
- \(3i + 2i - 4 = 18i\) \( \rightarrow \) (none of the options align with -4/13)
- \(2i + 3 = 2i - 5\) \( \rightarrow \) No Solution
- \(3(2i - 7) = 6i - 21\) \( \rightarrow \) Infinite Solutions

Thus, the best matches we have found are:
- \(3i + 2i - 4 = 18i\) - No direct match
- \(2i + 3 = 2i - 5\) - **No Solution**
- \(3(2i - 7) = 6i - 21\) - **Infinite Solutions**

To summarize in terms of the matching process:
- 3i + 2i - 4 = 18i -> No matched solution
- 2i + 3 = 2i - 5 -> No Solution
- 3(2i - 7) = 6i - 21 -> Infinite Solutions

Answer 3

Let's reevaluate each equation carefully to ensure accurate solutions.

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

Combine the terms on the left side:

\[
5i - 4 = 18i
\]

Now, isolate \(i\):

\[
-4 = 18i - 5i
\]

\[
-4 = 13i
\]

Therefore,

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

**Note**: This solution matched mathematically, but the value does not correspond with the provided options.

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

Subtract \(2i\) from both sides:

\[
3 = -5
\]

This statement is false, indicating that:

**No Solution**.

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

Expanding the left side:

\[
6i - 21 = 6i - 21
\]

This simplifies to an identity, implying that both sides are equal for all values of \(i\):

**Infinite Solutions**.

### Conclusion:
With careful reevaluation, the matching is as follows:
- \(3i + 2i - 4 = 18i\) \( \rightarrow \) (i = -4/13, not an option)
- \(2i + 3 = 2i - 5\) \( \rightarrow \) **No Solution**
- \(3(2i - 7) = 6i - 21\) \( \rightarrow \) **Infinite Solutions**

Therefore, the correct matches are:
- No Solution for \(2i + 3 = 2i - 5\)
- Infinite Solutions for \(3(2i - 7) = 6i - 21\)

The original equation \(3i + 2i - 4 = 18i\) does yield \(i = -\frac{4}{13}\), but it does not match any provided options.

Thank you for prompting me to double-check! Please let me know if you need any further clarification.