Match the equation with its solution.(3 points)
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3i+2i−4=18i
2i+3=2i−5
3(2i−7)=6i−21
1. 3i + 2i - 4 = 18i - Solution: i = -1/4
2. 2i + 3 = 2i - 5 - Solution: No solution
3. 3(2i - 7) = 6i - 21 - Solution: All real numbers are solutions
To determine the correct match between the equations and their solutions, let's solve each equation step-by-step:
1. 3i + 2i - 4 = 18i:
First, combine like terms on the left side:
(3i + 2i) - 4 = 18i
5i - 4 = 18i
Next, isolate the variable by moving all terms containing i to one side:
5i - 18i = 4
-13i = 4
Finally, solve for i by dividing both sides by -13:
i = 4 / -13
The solution for this equation is: i = -4/13
2. 2i + 3 = 2i - 5:
This equation does not have a solution.
When we simplify both sides, we get: 3 = -5, which is not a true statement. Therefore, no value of i can make this equation true.
3. 3(2i - 7) = 6i - 21:
First, distribute the 3 on the left side:
6i - 21 = 6i - 21
This equation is an identity, which means it is true for all real numbers. Therefore, any value of i can be a solution for this equation.
Matching the equations with their solutions:
1. 3i + 2i - 4 = 18i - i = -4/13
2. 2i + 3 = 2i - 5 - No Solution
3. 3(2i - 7) = 6i - 21 - All Real Numbers