. Match the equation with its solution.(3 points)

Question

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
3i+2i−4=18i
2i+3=2i−5
3(2i−7)=6i−21
The option "i is equal to negative 1 third" (6 of 6) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.

Answer 1

Let's go through each equation and solve for \( i \).

1. Equation: \( 3i + 2i - 4 = 18i \)
   Simplifying the left side: \[ 5i - 4 = 18i \] Rearranging gives: \[ -4 = 18i - 5i \] \[ -4 = 13i \] Thus, solving for \( i \): \[ i = -\frac{4}{13} \]

2. Equation: \( 2i + 3 = 2i - 5 \) Simplifying: \[ 3 = -5 \] This is a contradiction, meaning there is no solution for this equation.

3. Equation: \( 3(2i - 7) = 6i - 21 \) Expanding the left side: \[ 6i - 21 = 6i - 21 \] This is an identity, meaning every value of \( i \) is a solution.

Now, matching these with the options given:

• For the first equation \( 3i + 2i - 4 = 18i \), the solution is \( i = -\frac{4}{13} \).
• The second equation has no solution.
• The third equation has an infinite number of solutions.

Based on what you've provided, if "i is equal to negative 1 third" was one of the responses, it does not appear to match any of the equations correctly. Specifically, it does not match the results we calculated.

Please review the options available and match them correctly according to the calculations above. Let me know if there's anything else I can help with!