match the equation with the solution
3(2i-7)=6i-21
2i+3=2i-5
1) 3(2i-7)=6i-21 - Solution: i = -7/3
2) 2i+3=2i-5 - Solution: There is no solution
those arent the options
Apologies for the confusion. Here are the options and the correct match:
1. 3(2i-7)=6i-21 - Solution: i = -7/3
2. 2i+3=2i-5 - Solution: No solution
To match the equations with their solutions, we can solve each equation step-by-step.
Equation 1: 3(2i - 7) = 6i - 21
1. Distribute the 3 to the terms inside the parentheses:
6i - 21 = 6i - 21
2. As the equation is true for all values of i, there are infinitely many solutions.
Therefore, Equation 1 has infinitely many solutions.
Equation 2: 2i + 3 = 2i - 5
1. Subtract 2i from both sides to isolate the constant term:
2i - 2i + 3 = 2i - 2i - 5
3 = -5
2. As the equation is NOT true, there is no solution.
Therefore, Equation 2 has no solution.
To match the equation with the solution, we need to solve each equation separately and then match the obtained solution with the corresponding equation. Let's solve each equation step by step:
1. 3(2i - 7) = 6i - 21:
First, distribute the 3 to both terms inside the parentheses:
6i - 21 = 6i - 21
Now, notice that the variables cancel out on both sides of the equation. This means that any value for i would make the equation true. So, the equation 3(2i - 7) = 6i - 21 is true for any value of i. Therefore, the solution is all real numbers.
2. 2i + 3 = 2i - 5:
To solve this equation, we want to isolate the variable i on one side. Start by subtracting 2i from both sides to eliminate i from the right side of the equation:
2i - 2i + 3 = 2i - 2i - 5
3 = -5
This equation is not possible since 3 is not equal to -5. It means they are not equal, and we can't find any value for i that satisfies the equation. Therefore, the equation 2i + 3 = 2i - 5 has no solution.
To summarize:
- The equation 3(2i-7)=6i-21 has a solution of all real numbers.
- The equation 2i+3=2i-5 has no solution.