Question
How Many Solutions? Quick Check
3 of 5 3 of 5 Items
Question
Solve for x
x
to determine if the equation has one, none, or infinite solutions.
3(x+2)−6=3x
3
(
x
+
2
)
−
6
=
3
x
(1 point)
Responses
The equation has one solution: x=3
.
The equation has one solution: x equals 3 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−3
.
The equation has one solution: x equals negative 3 .
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Answers
GPT 3.5
The equation has one solution: x=3.
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Which of the following is an example of an equation with no solution?(1 point)
Responses
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
4x+3=3x+3
4 x plus 3 equals 3 x plus 3
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
3x+4=3x+3
Which of the following is an example of an equation with no solution?(1 point)
Responses
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
4x+3=3x+3
4 x plus 3 equals 3 x plus 3
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
3x+4=3x+3
GPT 3.5
The example of an equation with no solution is:
3x+4=3x+3
3x+4=3x+3
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Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
4x+3=4x+3
4 x plus 3 equals 4 x plus 3
3x+4=4x+3
Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
4x+3=4x+3
4 x plus 3 equals 4 x plus 3
3x+4=4x+3
GPT 3.5
The equation with exactly one solution is:
3x+4=3x+4
3x+4=3x+4
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Solve for x
to determine if the equation has one, none, or infinite solutions.
3(x+2)−6=3x
(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=3
.
The equation has one solution: x equals 3 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−3
.
Solve for x
to determine if the equation has one, none, or infinite solutions.
3(x+2)−6=3x
(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=3
.
The equation has one solution: x equals 3 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−3
.
GPT 3.5
To determine the number of solutions for the equation 3(x+2)−6=3x, we can simplify it:
3x + 6 - 6 = 3x
3x = 3x
This equation has infinitely many solutions because any value of x will make the equation true. Therefore, the correct response is:
The equation has infinite solutions.
3x + 6 - 6 = 3x
3x = 3x
This equation has infinitely many solutions because any value of x will make the equation true. Therefore, the correct response is:
The equation has infinite solutions.
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Solve for x
to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15
(1 point)
Responses
The equation has one solution: x=0
.
The equation has one solution: x equals 0 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−10
.
The equation has one solution: x equals negative 10 .
The equation has infinite solutions.
Solve for x
to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15
(1 point)
Responses
The equation has one solution: x=0
.
The equation has one solution: x equals 0 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−10
.
The equation has one solution: x equals negative 10 .
The equation has infinite solutions.
GPT 3.5
To solve the equation 4x=3(x+5)−15, let's start by simplifying the right side:
4x = 3x + 15 - 15
4x = 3x
Subtracting 3x from both sides, we get:
4x - 3x = 0
x = 0
The equation has one solution: x = 0.
4x = 3x + 15 - 15
4x = 3x
Subtracting 3x from both sides, we get:
4x - 3x = 0
x = 0
The equation has one solution: x = 0.
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Solve for x
to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6
(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=10
.
The equation has one solution: x equals 10 .
The equation has one solution: x=6
.
The equation has one solution: x equals 6 .
The equation has infinite solutions.
The equation has infinite solutions.
Solve for x
to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6
(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=10
.
The equation has one solution: x equals 10 .
The equation has one solution: x=6
.
The equation has one solution: x equals 6 .
The equation has infinite solutions.
The equation has infinite solutions.
GPT 3.5
To solve the equation 5(2x+2)−7x=3x+6, let's simplify both sides of the equation.
Starting with the left side:
5(2x+2)−7x = 10x + 10 - 7x = 3x + 10
Now, we have:
3x + 10 = 3x + 6
Subtracting 3x from both sides, we get:
10 = 6
This equation is not possible since 10 is not equal to 6. Therefore, the equation has no solution.
Starting with the left side:
5(2x+2)−7x = 10x + 10 - 7x = 3x + 10
Now, we have:
3x + 10 = 3x + 6
Subtracting 3x from both sides, we get:
10 = 6
This equation is not possible since 10 is not equal to 6. Therefore, the equation has no solution.
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GPT 3.5
Apologies for the confusion earlier. Let's reevaluate the responses:
- The equation has no solution.
- The equation has one solution: x=10.
- The equation has one solution: x=6.
- The equation has infinite solutions.
Based on the work we just did, the correct response is:
The equation has no solution.
Thank you for bringing this to my attention.
- The equation has no solution.
- The equation has one solution: x=10.
- The equation has one solution: x=6.
- The equation has infinite solutions.
Based on the work we just did, the correct response is:
The equation has no solution.
Thank you for bringing this to my attention.
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GPT 3.5
I'm glad I could assist you! I strive to provide accurate and helpful information. If you have any more questions or need further assistance, feel free to ask. Thank you for your kind words!
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Complete the equation so that it has no solution.(1 point)
5x+12=
x+9
Complete the equation so that it has no solution.(1 point)
5x+12=
x+9
GPT 3.5
To complete the equation so that it has no solution, we need to ensure that it results in an inconsistent equation.
We can do this by setting the coefficients of x to be equal and the constants to be different.
In this case, let's set the coefficients of x to be equal to 5, and the constants to be different.
Therefore, the completed equation would be:
5x + 12 = 5x + 13
We can do this by setting the coefficients of x to be equal and the constants to be different.
In this case, let's set the coefficients of x to be equal to 5, and the constants to be different.
Therefore, the completed equation would be:
5x + 12 = 5x + 13
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Complete the equation so that it has no solution.(1 point)
−7x−12=
x+12
Complete the equation so that it has no solution.(1 point)
−7x−12=
x+12
GPT 3.5
To complete the equation so that it has no solution, we can set the coefficients of x to be opposite and the constants to be equal.
In this case, let's set the coefficients of x to be opposite, which means we'll have a positive 1 on the right side of the equation.
Therefore, the completed equation would be:
-7x - 12 = -x + 12
In this case, let's set the coefficients of x to be opposite, which means we'll have a positive 1 on the right side of the equation.
Therefore, the completed equation would be:
-7x - 12 = -x + 12
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But that answer is wrong
GPT 3.5
Apologies for the incorrect response. To complete the equation so that it has no solution, we can set the coefficients of x to be equal and the constants to be different, similar to the previous example.
In this case, let's set the coefficients of x to be equal to -1, and the constants to be different.
Therefore, the completed equation would be:
-7x - 12 = -x + 13
In this case, let's set the coefficients of x to be equal to -1, and the constants to be different.
Therefore, the completed equation would be:
-7x - 12 = -x + 13
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Solve for x to determine if the equation has one, none, or infinite solutions.
6(2x+4)−24=12x
(1 point)
Responses
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−20.
6(2x+4)−24=12x
(1 point)
Responses
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−20.
GPT 3.5
To solve the equation 6(2x+4)−24=12x, let's simplify both sides of the equation.
First, distribute 6 to the terms inside the parentheses:
12x + 24 - 24 = 12x
Now, simplify the equation:
12x = 12x
This equation has the same terms on both sides, indicating that it has infinite solutions. Therefore, the correct response is:
The equation has infinite solutions.
First, distribute 6 to the terms inside the parentheses:
12x + 24 - 24 = 12x
Now, simplify the equation:
12x = 12x
This equation has the same terms on both sides, indicating that it has infinite solutions. Therefore, the correct response is:
The equation has infinite solutions.
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Solve for x
to determine if the equation has one, none, or infinite solutions.
9(x+1)=3(5x+1)−12
(1 point)
Responses
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=3
.
The equation has one solution: x equals 3 .
The equation has one solution: x=0
.
The equation has one solution: x equals 20 .
The equation has no solution.
The equation has no solution.
to determine if the equation has one, none, or infinite solutions.
9(x+1)=3(5x+1)−12
(1 point)
Responses
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=3
.
The equation has one solution: x equals 3 .
The equation has one solution: x=0
.
The equation has one solution: x equals 20 .
The equation has no solution.
The equation has no solution.
GPT 3.5
To solve the equation 9(x+1)=3(5x+1)−12, let's simplify both sides of the equation.
First, distribute on both sides:
9x + 9 = 15x + 3 - 12
Simplifying further, we have:
9x + 9 = 15x - 9
Next, let's isolate the x term on one side of the equation. Subtracting 15x from both sides, we get:
-6x + 9 = -9
Subtracting 9 from both sides, we have:
-6x = -18
Now, divide both sides by -6:
x = 3
The equation has one solution: x = 3.
First, distribute on both sides:
9x + 9 = 15x + 3 - 12
Simplifying further, we have:
9x + 9 = 15x - 9
Next, let's isolate the x term on one side of the equation. Subtracting 15x from both sides, we get:
-6x + 9 = -9
Subtracting 9 from both sides, we have:
-6x = -18
Now, divide both sides by -6:
x = 3
The equation has one solution: x = 3.