Question

Match the equation with its solution.(3 points)

2i+3=2i−5
3i+2i−4=18i
3(2i−7)=6i−21

Answer 1

[AI-generated answer — Bot GPT 3.5]

1. 2i+3=2i−5 - This equation has no solution.

2. 3i+2i−4=18i - The solution to this equation is 3.

3. 3(2i−7)=6i−21 - The solution to this equation is -6.

Answer 2

The last two answers are wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the incorrect answers. Let's re-evaluate the equations:

1. 2i+3=2i−5
Begin by subtracting 2i from both sides to isolate the constant term:
3 = -5
This equation has no solution because the left side does not equal the right side.

2. 3i+2i−4=18i
Combine like terms on the left side of the equation:
5i - 4 = 18i
To isolate i, subtract 5i from both sides:
-4 = 13i
Divide both sides by 13 to solve for i:
i = -4/13

3. 3(2i−7)=6i−21
Distribute on the left side of the equation:
6i - 21 = 6i - 21
This equation is an identity, meaning that it is true for all values of i. There is no specific solution.

Answer 4

[AI-generated answer — Step-by-Step Bot]

To match the equations with their solutions, we will solve each equation step-by-step.

Equation 1: 2i + 3 = 2i - 5
Subtracting 2i from both sides:
3 = -5

Since 3 does not equal -5, this equation has no solution.

Equation 2: 3i + 2i - 4 = 18i
Combining like terms:
5i - 4 = 18i
Subtracting 5i from both sides:
-4 = 13i
Dividing both sides by 13:
i = -4/13

The solution to Equation 2 is i = -4/13.

Equation 3: 3(2i - 7) = 6i - 21
Distributing the 3:
6i - 21 = 6i - 21
This equation is an identity, as the terms on both sides are the same.

Since it is not possible to match this equation with a single solution, we can say that the solution to the equation is all real numbers.

Summary:

Equation 1: No solution
Equation 2: i = -4/13
Equation 3: All real numbers

Answer 5

[AI-generated answer — Explain Bot]

To match the equations with their solutions, we need to solve each equation to find the value of the variable (i).

1. 2i + 3 = 2i - 5
To solve this equation, we want to isolate the variable (i) on one side. Notice that there is (2i) on both sides of the equation, so we can subtract (2i) from both sides:
2i - 2i + 3 = 2i - 2i - 5
This simplifies to:
3 = -5
Since this equation does not have a valid solution (a contradiction), there is no solution for the equation.

2. 3i + 2i - 4 = 18i
We want to combine the like terms on the left side of the equation:
5i - 4 = 18i
To isolate the variable (i), we can subtract 5i from both sides:
5i - 5i - 4 = 18i - 5i
This simplifies to:
-4 = 13i
To solve for i, we can divide both sides by 13:
-4/13 = 13i/13
This gives us the solution:
i = -4/13

3. 3(2i - 7) = 6i - 21
To solve this equation, we will distribute the 3 to both terms within the parentheses:
6i - 21 = 6i - 21
Notice that both sides of the equation are the same. Therefore, any value of i will make this equation true. In other words, this equation has infinitely many solutions.