Match the equation with its solution.(5 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.
3i+2i−7=18
3(2i−7)=15
3i+5=2i−7
3i+5=3i+7
3(2i+7)=6i+21
3i+2i-7=18
Solution: i = 5
3(2i-7)=15
Solution: i = 4
3i+5=2i-7
Solution: i = -12
3i+5=3i+7
Solution: No solution
3(2i+7)=6i+21
Solution: All real numbers
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
Let's solve the given equations and match them with their solutions.
1. 3i + 2i - 7 = 18
Simplifying the left side of the equation we get:
5i - 7 = 18
Adding 7 to both sides:
5i = 25
Dividing both sides by 5:
i = 5
2. 3(2i - 7) = 15
Distributing the 3 on the left side:
6i - 21 = 15
Adding 21 to both sides:
6i = 36
Dividing both sides by 6:
i = 6
3. 3i + 5 = 2i - 7
Subtracting 2i from both sides:
i + 5 = -7
Subtracting 5 from both sides:
i = -12
4. 3i + 5 = 3i + 7
This equation is inconsistent since no value of i can satisfy it.
5. 3(2i + 7) = 6i + 21
Distributing the 3 on the left side:
6i + 21 = 6i + 21
This equation is an identity and holds true for all values of i.
Matching the equations with their solutions:
1. 3i + 2i - 7 = 18 --> i = 5
2. 3(2i - 7) = 15 --> i = 6
3. 3i + 5 = 2i - 7 --> i = -12
4. 3i + 5 = 3i + 7 --> No solution
5. 3(2i + 7) = 6i + 21 --> Identity
To match the equation with its solution, we need to solve each equation and find the value of "i" that makes the equation true. Let's solve each equation one by one:
Equation 1: 3i + 2i - 7 = 18
Combine like terms: 5i - 7 = 18
Add 7 to both sides: 5i = 25
Divide both sides by 5: i = 5
So, the solution to equation 1 is i = 5.
Equation 2: 3(2i - 7) = 15
Distribute the 3: 6i - 21 = 15
Add 21 to both sides: 6i = 36
Divide both sides by 6: i = 6
So, the solution to equation 2 is i = 6.
Equation 3: 3i + 5 = 2i - 7
Subtract 2i from both sides: i + 5 = -7
Subtract 5 from both sides: i = -12
So, the solution to equation 3 is i = -12.
Equation 4: 3i + 5 = 3i + 7
Subtract 3i from both sides: 5 = 7
This equation has no solution because the equation simplifies to a false statement (5 = 7).
Equation 5: 3(2i + 7) = 6i + 21
Distribute the 3: 6i + 21 = 6i + 21
The equation is true for all values of "i". There are infinitely many solutions.
So, to match the equation with its solution:
- Equation 1 matches with Solution i = 5.
- Equation 2 matches with Solution i = 6.
- Equation 3 matches with Solution i = -12.
- Equation 4 has no solution.
- Equation 5 matches with infinitely many solutions.