Complete the equation so that it has no solution.(1 point)
5x+12= __x+9
To make the equation have no solution, we need to set the coefficients of the x's on both sides of the equation equal to each other, but the constant term (the number without x) unequal to each other.
Therefore, the missing number is 9, and the complete equation is:
5x + 12 = 9x + 9
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=−20.
The equation has one solution: x equals negative 20 .
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
To determine if the equation has one, none, or infinite solutions, we need to solve for x.
6(2x + 4) - 24 = 12x
First, distribute the 6:
12x + 24 - 24 = 12x
Combine like terms:
12x = 12x
The variable x cancels out. This means that the equation is an identity and holds true for any value of x. Therefore, the equation has infinite solutions.
Which of the following is an example of an equation with no solution?(1 point)
Responses
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
4x+3=3x+3
4 x plus 3 equals 3 x plus 3
3x+4=3x+4
The equation "3x + 4 = 3x + 4" is an example of an equation with no solution.
This is because when we subtract 3x from both sides, we are left with 4 = 4. This equation is an identity and is always true, no matter the value of x. Therefore, there are no specific x-values that satisfy this equation, leading to no solution.
Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
4x+3=4x+3
4 x plus 3 equals 4 x plus 3
3x+4=3x+4
The equation "3x + 4 = 4x + 3" is an example of an equation with exactly one solution.
This equation can be solved by isolating the variable x. When we subtract 3x from both sides, we get 4 = x + 3. Then, by subtracting 3 from both sides, we have 1 = x.
Therefore, x has exactly one solution in this equation: x = 1.
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 one solution: x=3.
The equation has one solution: x equals 3 .
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−3.
To determine if the equation has one, none, or infinite solutions, we need to solve for x.
3(x + 2) - 6 = 3x
First, distribute the 3:
3x + 6 - 6 = 3x
Combine like terms:
3x = 3x
The variable x cancels out. This means that the equation is an identity and holds true for any value of x. Therefore, 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 no solution.
The equation has no solution.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=−10.
The equation has one solution: x equals negative 10 .