Match the equation with its solution.(5 points)
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3i+2i−7=18
3(2i−7)=15
3i+5=2i−7
3i+5=3i+7
3(2i+7)=6i+21
Equation: 3i+2i−7=18
Solution: i = 5
Equation: 3(2i−7)=15
Solution: i = 6
Equation: 3i+5=2i−7
Solution: No solution
Equation: 3i+5=3i+7
Solution: No solution
Equation: 3(2i+7)=6i+21
Solution: All real numbers
Ur last two answers are wrong bot
Let's go through each equation and match it with its solution:
1. Equation: 3i+2i−7=18
Solution: 3(2i−7)=15
2. Equation: 3i+5=2i−7
Solution: No solution
3. Equation: 3i+5=3i+7
Solution: No solution
4. Equation: 3(2i+7)=6i+21
Solution: True for all values of i
Therefore, the correct matches are:
1. 3i+2i−7=18 --> Solution: 3(2i−7)=15
2. 3i+5=2i−7 --> Solution: No solution
3. 3i+5=3i+7 --> Solution: No solution
4. 3(2i+7)=6i+21 --> Solution: True for all values of i
To match each equation with its solution, we can solve each equation one by one to find the corresponding solution. Let's go through each equation:
1. 3i + 2i - 7 = 18
To solve this equation, we group the like terms:
(3i + 2i) - 7 = 18
5i - 7 = 18
Next, we isolate the variable:
5i = 18 + 7
5i = 25
Finally, we solve for i by dividing both sides by 5:
i = 25/5
i = 5
So, the solution for equation 1 is i = 5.
2. 3(2i - 7) = 15
To solve this equation, we distribute 3 to the terms inside the parentheses:
6i - 21 = 15
Next, we isolate the variable:
6i = 15 + 21
6i = 36
Finally, we solve for i by dividing both sides by 6:
i = 36/6
i = 6
So, the solution for equation 2 is i = 6.
3. 3i + 5 = 2i - 7
To solve this equation, we isolate the variable by subtracting 2i from both sides:
3i - 2i + 5 = -7
Simplifying, we get:
i + 5 = -7
Next, we isolate the variable by subtracting 5 from both sides:
i = -7 - 5
i = -12
So, the solution for equation 3 is i = -12.
4. 3i + 5 = 3i + 7
To solve this equation, we subtract 3i from both sides:
3i - 3i + 5 = 3i - 3i + 7
5 = 7
This is a contradiction because 5 does not equal 7. Therefore, this equation has no solution.
So, the solution for equation 4 is "No solution".
5. 3(2i + 7) = 6i + 21
To solve this equation, we distribute 3 to the terms inside the parentheses:
6i + 21 = 6i + 21
This equation is an identity because both sides are equal, regardless of the value of i. Therefore, this equation has infinitely many solutions.
So, the solution for equation 5 is "Infinitely many solutions".
To summarize the matches:
Equation 1: Solution is i = 5
Equation 2: Solution is i = 6
Equation 3: Solution is i = -12
Equation 4: No solution
Equation 5: Infinitely many solutions