Match the equation with its solution(s).(5 points)
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3i+5=3i+7
3(2i−7)=15
3i+5=2i−7
3(2i+7)=6i+21
3i+2i−7=18
1. 3i+5=3i+7 - No solution (Contradiction)
2. 3(2i−7)=15 - i = 8
3. 3i+5=2i−7 - i = -12
4. 3(2i+7)=6i+21 - i = -14
5. 3i+2i−7=18 - i = 25
these answers arent correct can you give the correct answers
Apologies for the incorrect answers. Here are the correct matches:
1. 3i+5=3i+7 - No solution (Contradiction)
2. 3(2i−7)=15 - i = 12
3. 3i+5=2i−7 - i = -12
4. 3(2i+7)=6i+21 - i = -7
5. 3i+2i−7=18 - i = 25
Let's analyze each equation and its solution(s):
1. 3i + 5 = 3i + 7
Subtracting 3i from both sides, we get:
5 = 7
This equation is not possible, as it leads to a contradiction. There is no solution.
2. 3(2i − 7) = 15
Simplifying the left side, we have:
6i − 21 = 15
Adding 21 to both sides, we get:
6i = 36
Dividing both sides by 6, we find:
i = 6
The solution to this equation is i = 6.
3. 3i + 5 = 2i − 7
Subtracting 2i from both sides, we get:
i + 5 = -7
Subtracting 5 from both sides, we have:
i = -12
The solution to this equation is i = -12.
4. 3(2i + 7) = 6i + 21
Simplifying the left side, we have:
6i + 21 = 6i + 21
This equation is always true, no matter the value of i. It has infinite solutions.
5. 3i + 2i − 7 = 18
Combining like terms, we get:
5i - 7 = 18
Adding 7 to both sides, we have:
5i = 25
Dividing both sides by 5, we find:
i = 5
The solution to this equation is i = 5.
To match the equation with its solution(s):
Equation 1: No solution
Equation 2: i = 6
Equation 3: i = -12
Equation 4: Infinite solutions
Equation 5: i = 5