Match the equation with its solution.(3 points)

Question

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. \(3i + 2i - 4 = 18i\) → \(i = -\frac{4}{13}\)