Match the equation with its solution.(3 points)

Question

Match the equation with its solution.(3 points)

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3i+2i−4=18i
3(2i−7)=6i−21
2i+3=2i−5

Answer 1

3i+2i−4=18i: No solution

3(2i−7)=6i−21: 2
2i+3=2i−5: No solution

Answer 2

To match the given equations with their solutions, we need to solve each equation and then match the solution with the correct equation. Let's solve each equation one by one:

1) 3i + 2i - 4 = 18i

Combine like terms:
5i - 4 = 18i

Move all terms containing 'i' to one side and all constant terms to the other side:
5i - 18i = 4

Combine like terms again:
-13i = 4

To solve for 'i', divide both sides of the equation by -13:
i = 4 / -13

The solution to this equation is i = 4 / -13.

2) 3(2i - 7) = 6i - 21

Apply the distributive property:
6i - 21 = 6i - 21

The left side and right side of the equation are the same, so this equation is an identity.

The solution to this equation is any value for 'i' since it's an identity.

3) 2i + 3 = 2i - 5

Subtract 2i from both sides:
3 = -5

The left side and right side of the equation are not equal, so this equation has no solution.

Now, let's match the equations with their solutions:

1) 3i + 2i - 4 = 18i - Solution: i = 4 / -13
2) 3(2i - 7) = 6i - 21 - Solution: Any value for i
3) 2i + 3 = 2i - 5 - Solution: No solution

Therefore, the correct matches are:
- Equation 1 matches with Solution 1
- Equation 2 matches with Solution 2
- Equation 3 matches with Solution 3

Answer 3

Let's solve each equation step-by-step:

1) 3i + 2i - 4 = 18i

Combine like terms on the left side:
5i - 4 = 18i

Move all terms involving the variable to one side:
5i - 18i = 4

Combine like terms on the left side:
-13i = 4

Divide both sides by -13 to solve for i:
i = -4/13

2) 3(2i - 7) = 6i - 21

Distribute the 3 to the terms inside the parentheses:
6i - 21 = 6i - 21

Since the equation is the same on both sides, it is an identity. This means that the equation is true for all values of i.

3) 2i + 3 = 2i - 5

Subtract 2i from both sides to eliminate the variable:
3 = -5

This is a contradiction since 3 is not equal to -5. Therefore, there is no solution for this equation.