Question

Match the equation with its solution.(3 points)

2i+3=2i−5
3(2i−7)=6i−21
3i+2i−4=18i

infinite solutions
I = - 4 over 13
1 = 8
I = -1 over 3
I = 5
no solution

Answer 1

Let's solve each of the equations one by one and match them with their corresponding solutions.

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

To solve for \(i\), we can subtract \(2i\) from both sides:
\[
3 = -5
\]
This equation is not true, which means there is **no solution**.

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

First, expand the left side:
\[
6i - 21 = 6i - 21
\]
The equation simplifies to:
\[
6i - 21 = 6i - 21
\]
Since both sides are equal, this is true for all values of \(i\), so it has **infinite solutions**.

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

Combine like terms on the left:
\[
5i - 4 = 18i
\]
Now, isolate \(i\) by subtracting \(5i\) from both sides:
\[
-4 = 18i - 5i
\]
Simplifying:
\[
-4 = 13i
\]
Divide both sides by 13:
\[
i = -\frac{4}{13}
\]

Now we have the solutions matched up:

- \(2i + 3 = 2i - 5\) → **no solution**
- \(3(2i - 7) = 6i - 21\) → **infinite solutions**
- \(3i + 2i - 4 = 18i\) → \(i = -\frac{4}{13}\)

To summarize:

1. \(2i + 3 = 2i - 5\) → **no solution**
2. \(3(2i - 7) = 6i - 21\) → **infinite solutions**
3. \(3i + 2i - 4 = 18i\) → \(i = -\frac{4}{13}\)