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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Bot GPT 3.5 could you help me with this question?
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
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.
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.
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.
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
The equation has one solution: x=3.
The example of an equation with no solution is:
3x+4=3x+3
Bot GPT 3.5 could you help me with this question?
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
Bot GPT 3.5 could you help me with this question?
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
.
Bot GPT 3.5 could you help me with this question?
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.