Match the equation with its solution.(3 points)
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.
2i+3=2i−5
3i+2i−4=18i
3(2i−7)=6i−21
The first equation, 2i+3=2i−5, has no solution.
The second equation, 3i+2i−4=18i, has no solution.
The third equation, 3(2i−7)=6i−21, has a solution of i=−3.
To match the equations with their solutions, we will solve each equation step-by-step and see which solution matches the given equations.
1) 2i + 3 = 2i - 5
To solve this equation, we want to isolate the variable "i" on one side of the equation. Let's start by simplifying both sides of the equation:
2i + 3 = 2i - 5
Subtract 2i from both sides of the equation:
2i - 2i + 3 = 2i - 2i - 5
This simplifies to:
3 = -5
The equation -5 = 3 is not true, so the solution to this equation is not valid. So, we can eliminate this option as a solution.
2) 3i + 2i - 4 = 18i
Let's simplify both sides of the equation:
5i - 4 = 18i
Next, subtract 5i from both sides of the equation:
5i - 5i - 4 = 18i - 5i
This simplifies to:
-4 = 13i
Divide both sides of the equation by 13:
-4/13 = 13i/13
This simplifies to:
-4/13 = i
So, the solution to this equation is i = -4/13.
3) 3(2i - 7) = 6i - 21
Start by simplifying both sides of the equation:
6i - 21 = 6i - 21
The equation is the same on both sides, so this equation is true for all values of i. Therefore, any value of i can be a solution to this equation.
In summary, the equations and their solutions are:
1) 2i + 3 = 2i - 5 --> No solution
2) 3i + 2i - 4 = 18i --> i = -4/13
3) 3(2i - 7) = 6i - 21 --> Any value of i is a solution.
To match the equations with their solutions, let's solve each equation step by step:
1) 2i + 3 = 2i - 5
Moving the variables to one side and the constants to the other side:
2i - 2i = -5 - 3
0 = -8
Since there is no solution to this equation, we can match it with "No Solution."
2) 3i + 2i - 4 = 18i
Combining like terms:
5i - 4 = 18i
Moving all the variables to one side:
5i - 18i = 4
-13i = 4
Dividing both sides by -13:
i = -4/13
So, this equation can be matched with "i = -4/13."
3) 3(2i - 7) = 6i - 21
Distributing 3 to the terms within the parentheses:
6i - 21 = 6i - 21
The equation on both sides is the same, which means it is true for all values of i. Thus, this equation can be matched with "All Real Numbers."
Therefore, the matching equations and solutions are:
1) 2i + 3 = 2i - 5 => No Solution
2) 3i + 2i - 4 = 18i => i = -4/13
3) 3(2i - 7) = 6i - 21 => All Real Numbers