Match the equation with its solution(s).(5 points)
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3i+5=2i−7
3(2i−7)=15
3(2i+7)=6i+21
3i+5=3i+7
3i+2i−7=18
3i+5=2i−7: No solution
3(2i−7)=15: i = 8
3(2i+7)=6i+21: i = -4
3i+5=3i+7: No solution
3i+2i−7=18: i = 5
no
Match the equation with its solution.(3 points)
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3(2i−7)=6i−21
3i+2i−4=18i
2i+3=2i−5
can you answer the question above me bot?
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.
3(2i−7)=6i−21
3i+2i−4=18i
2i+3=2i−5
To match the equations with their solutions, let's go through each equation:
1) 3i+5=2i−7
To solve this equation, we can start by isolating the variable on one side of the equation:
3i - 2i = -7 - 5
i = -12
2) 3(2i−7)=15
We can distribute the 3 to both terms inside the parentheses:
6i - 21 = 15
Adding 21 to both sides gives us:
6i = 36
Dividing both sides by 6 yields:
i = 6
3) 3(2i+7)=6i+21
Again, distribute the 3 to both terms inside the parentheses:
6i + 21 = 6i + 21
This equation does not involve the variable "i" and is always true. So, it is an identity equation and its solutions are all real numbers.
4) 3i+5=3i+7
Subtracting 3i from both sides gives us:
5 = 7
This equation is contradictory and has no solution.
5) 3i+2i−7=18
Combining like terms on the left side:
5i - 7 = 18
Adding 7 to both sides gives us:
5i = 25
Dividing both sides by 5 yields:
i = 5
Now matching each equation to its solution:
1) 3i+5=2i−7 -> i = -12
2) 3(2i−7)=15 -> i = 6
3) 3(2i+7)=6i+21 -> Identity equation, all real numbers are solutions.
4) 3i+5=3i+7 -> No solution.
5) 3i+2i−7=18 -> i = 5
To match the equation with its solution(s), we can solve each equation and see which solution(s) match the equation.
Let's solve each equation one by one:
1) 3i + 5 = 2i - 7
Subtract 2i from both sides to eliminate the i term:
3i - 2i + 5 = -7
Simplifying further:
i + 5 = -7
Subtract 5 from both sides:
i = -12
Solution to equation 1: i = -12
2) 3(2i - 7) = 15
Distribute the 3 on the left side:
6i - 21 = 15
Add 21 to both sides:
6i = 36
Divide both sides by 6:
i = 6
Solution to equation 2: i = 6
3) 3(2i + 7) = 6i + 21
Distribute the 3 on the left side:
6i + 21 = 6i + 21
Both sides of the equation are the same, so this equation is true for all values of i.
Solution to equation 3: All real numbers are solutions.
4) 3i + 5 = 3i + 7
Subtract 3i from both sides to eliminate the i term:
5 = 7
This equation is not possible, since 5 does not equal 7.
5) 3i + 2i - 7 = 18
Combine like terms:
5i - 7 = 18
Add 7 to both sides:
5i = 25
Divide both sides by 5:
i = 5
Solution to equation 5: i = 5
Now, let's match the equations with their corresponding solutions:
Equation 1: 3i + 5 = 2i - 7
Solution 1: i = -12
Equation 2: 3(2i - 7) = 15
Solution 2: i = 6
Equation 3: 3(2i + 7) = 6i + 21
Solution 3: All real numbers are solutions.
Equation 4: 3i + 5 = 3i + 7
Solution 4: No solution
Equation 5: 3i + 2i - 7 = 18
Solution 5: i = 5